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FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n>0$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n>0$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also, if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

And, if we write $x(n)$ and $y(n)$ for the alternating smallest and biggest one of $w(n)$ and $g(n)$ then

$x(n) = n * (n - 1) / 2$

and

$y(n) = n * (n + 1) / 2$

FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n==1$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n==1$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also, if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

And, if we write $x(n)$ and $y(n)$ for the alternating smallest and biggest one of $w(n)$ and $g(n)$ then

$x(n) = n * (n - 1) / 2$

and

$y(n) = n * (n + 1) / 2$

FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n>0$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n>0$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also, if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

And, if we write $x(n)$ and $y(n)$ for the alternating smallest and biggest one of $w(n)$ and $g(n)$ then

$x(n) = (n^2 - n) / 2$

and

$y(n) = (n^2 + n) / 2$

FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n>0$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n>0$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also, if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

And, if we write $x(n)$ and $y(n)$ for the alternating smallest and biggest one of $w(n)$ and $g(n)$ then

$x(n) = n * (n - 1) / 2$

and

$y(n) = n * (n + 1) / 2$

FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n>0$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n>0$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

FYI

Given @cap's clever visualization solution, following recursive formulas:

• number $g(n)$ of grey triangles

$g(n)=n>0$ $?$ $1:g(n-1)+(2*n-1)*(n\%2)$

• total number $t(n)$ of triangles

$t(n)=n>0$ $?$ $1:t(n-1)+(2*n-1)$

confirm $45\%$ for $n=10$

I found no OEIS® entry for grey, white or total series.

The highest amount $n$ of rows with an integer percentage $p$ of grey ones seems:

$n=50$ with $p=49\%$

Also, if we write $w(n)$ for number of white triangles, then following non-recursive equations hold

$t(n) = g(n) + w(n) = n^2$

and

$w(n) - g(n) = (-1)^n * n$

And, if we write $x(n)$ and $y(n)$ for the alternating smallest and biggest one of $w(n)$ and $g(n)$ then

$x(n) = (n^2 - n) / 2$

and

$y(n) = (n^2 + n) / 2$