A219078 - OEIS

A219078

T(n,k) = number of n X k binary arrays with every 0 a horizontal, diagonal or antidiagonal neighbor to some 1, n >= 1, k >= 1, read by antidiagonals.

1, 3, 1, 5, 11, 1, 9, 47, 41, 1, 17, 165, 337, 149, 1, 31, 625, 2321, 2469, 547, 1, 57, 2435, 17537, 32945, 18499, 2007, 1, 105, 9367, 134809, 494713, 477309, 137251, 7361, 1, 193, 35901, 1023441, 7561349, 14228041, 6879341, 1019123, 27001, 1, 355, 137865

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Original definition: T(n,k) = Hilltop maps: number of n X k binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, diagonal or antidiagonal neighbor in a random 0..1 n X k array.

Number of dominating sets in an n X k grid graph with edges connecting horizontally, diagonally or antidiagonally adjacent vertices. - Andrew Howroyd, Jul 14 2026

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..197

Eric Weisstein's World of Mathematics, Dominating Set.

EXAMPLE

Table starts:

1 3 5 9 17 31

1 11 47 165 625 2435

1 41 337 2321 17537 134809

1 149 2469 32945 494713 7561349

1 547 18499 477309 14228041 433704331

1 2007 137251 6879341 407374825 24734141495

1 7361 1019123 99118753 11660290321 1410242020653