diff --git a/tech/pascals_triangle.wiki b/tech/pascals_triangle.wiki index 1d81ebc..d7930b9 100644 --- a/tech/pascals_triangle.wiki +++ b/tech/pascals_triangle.wiki @@ -18,4 +18,11 @@ can be calculated via * The sum of the square of the elements of row `n` is equal to the middle element of row `2n` * 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]] diff --git a/tech/triagnular_numbers.wiki b/tech/triagnular_numbers.wiki new file mode 100644 index 0000000..7f8ba47 --- /dev/null +++ b/tech/triagnular_numbers.wiki @@ -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... + }}}