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Update for 03-03-22 23:30

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Tyler Perkins 2022-03-03 23:30:01 -05:00
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tech/pascals_triangle.wiki
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@ -18,4 +18,11 @@ can be calculated via
* The sum of the square of the elements of row `n` is equal to the middle * The sum of the square of the elements of row `n` is equal to the middle
element of row `2n` element of row `2n`
* For some row `n` where `n` is prime, all terms in that row except for the 1s * For some row `n` where `n` is prime, all terms in that row except for the 1s
are multiples of `p` are multiples of `n`
* To count odd terms in a row `n`, convert `n` to binary. Let `x` be the number
of 1s in the binary value (popcnt) Then the number of odd terms will be `2^x`
These values are known as [[goulds_sequence]]
* Every entry in row `2^(n-1) for n>=0` is odd.
* Diagonals along left and right edges contain only 1s
* Diagonals next to the edge of the diagonals count upward
* Next diagonal inward contains the [[triagnular_numbers]]

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tech/triagnular_numbers.wiki Normal file
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@ -0,0 +1,12 @@
= Triangular Numbers =
Triangular numbers are the number of objects arranged in an equilateral
triangle.
The first few are
{{{
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171,
190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595,
630, 666...
}}}