A392176 Array A(n,k) = (n*k-1)*(n*k-2)/2 (n>=1, k>=1) read by antidiagonals.

0, 0, 0, 1, 3, 1, 3, 10, 10, 3, 6, 21, 28, 21, 6, 10, 36, 55, 55, 36, 10, 15, 55, 91, 105, 91, 55, 15, 21, 78, 136, 171, 171, 136, 78, 21, 28, 105, 190, 253, 276, 253, 190, 105, 28, 36, 136, 253, 351, 406, 406, 351, 253, 136, 36, 45, 171, 325, 465, 561, 595, 561, 465, 325, 171, 45, 55, 210, 406, 595, 741, 820, 820, 741, 595, 406, 210, 55

Offset

1,5

Links

Table of n, a(n) for n=1..78.

David O. H. Cutler, Jonas Karlsson, and Neil J. A. Sloane, Cutting a Pancake with an Exotic Knife, arXiv:2511.15864[math.CO], v3, April 19 2026.

Example

The first few antidiagonals:
   0;
   0,  0;
   1,  3,   1;
   3, 10,  10,   3;
   6, 21,  28,  21,   6;
  10, 36,  55,  55,  36,  10;
  15, 55,  91, 105,  91,  55, 15;
  21, 78, 136, 171, 171, 136, 78, 21;
  ...
Array begins:
   0,   0,   1,   3,    6,   10,   15,   21,   28,   36,   45,   55, ...
   0,   3,  10,  21,   36,   55,   78,  105,  136,  171,  210,  253, ...
   1,  10,  28,  55,   91,  136,  190,  253,  325,  406,  496,  595, ...
   3,  21,  55, 105,  171,  253,  351,  465,  595,  741,  903, 1081, ...
   6,  36,  91, 171,  276,  406,  561,  741,  946, 1176, 1431, 1711, ...
  10,  55, 136, 253,  406,  595,  820, 1081, 1378, 1711, 2080, 2485, ...
  15,  78, 190, 351,  561,  820, 1128, 1485, 1891, 2346, 2850, 3403, ...
  21, 105, 253, 465,  741, 1081, 1485, 1953, 2485, 3081, 3741, 4465, ...
  28, 136, 325, 595,  946, 1378, 1891, 2485, 3160, 3916, 4753, 5671, ...
  36, 171, 406, 741, 1176, 1711, 2346, 3081, 3916, 4851, 5886, 7021, ...

Mathematica

Table[(#*k - 1)*(#*k - 2)/2 &[n - k + 1], {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Jan 23 2026 *)

Crossrefs

Sequence in context: A067329 A170860 A170845 * A375720 A025238 A289066

Adjacent sequences: A392173 A392174 A392175 * A392177 A392178 A392179

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 23 2026

Status

approved