A392176 - OEIS

%I #16 Apr 22 2026 07:40:46

%S 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,

%T 55,15,21,78,136,171,171,136,78,21,28,105,190,253,276,253,190,105,28,

%U 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

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

%H David O. H. Cutler, Jonas Karlsson, and Neil J. A. Sloane, <a href="https://arxiv.org/abs/2511.15864">Cutting a Pancake with an Exotic Knife</a>, arXiv:2511.15864[math.CO], v3, April 19 2026.

%e The first few antidiagonals:

%e    0;

%e    0,  0;

%e    1,  3,   1;

%e    3, 10,  10,   3;

%e    6, 21,  28,  21,   6;

%e   10, 36,  55,  55,  36,  10;

%e   15, 55,  91, 105,  91,  55, 15;

%e   21, 78, 136, 171, 171, 136, 78, 21;

%e   ...

%e Array begins:

%e    0,   0,   1,   3,    6,   10,   15,   21,   28,   36,   45,   55, ...

%e    0,   3,  10,  21,   36,   55,   78,  105,  136,  171,  210,  253, ...

%e    1,  10,  28,  55,   91,  136,  190,  253,  325,  406,  496,  595, ...

%e    3,  21,  55, 105,  171,  253,  351,  465,  595,  741,  903, 1081, ...

%e    6,  36,  91, 171,  276,  406,  561,  741,  946, 1176, 1431, 1711, ...

%e   10,  55, 136, 253,  406,  595,  820, 1081, 1378, 1711, 2080, 2485, ...

%e   15,  78, 190, 351,  561,  820, 1128, 1485, 1891, 2346, 2850, 3403, ...

%e   21, 105, 253, 465,  741, 1081, 1485, 1953, 2485, 3081, 3741, 4465, ...

%e   28, 136, 325, 595,  946, 1378, 1891, 2485, 3160, 3916, 4753, 5671, ...

%e   36, 171, 406, 741, 1176, 1711, 2346, 3081, 3916, 4851, 5886, 7021, ...

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

%K nonn,tabl

%O 1,5

%A _N. J. A. Sloane_, Jan 23 2026