A365469 Number of n X n nonnegative integer arrays with upper left entry 0, lower right entry n - 6, every value within 5 of its king-move distance from the upper left, and every value increasing by 0 or 1 with every step right, diagonally southeast, or down.

0, 0, 0, 0, 0, 1, 923, 414638, 141905658, 44926520946, 14490345222595, 4982468227997168, 1856518533812384105, 750167381136816327009, 326628155352701098746754, 151933161224857150407326456, 74864085012461648054019799968, 38785037369022058785365519932029

Offset

1,7

Links

Table of n, a(n) for n=1..18.

Robert Dougherty-Bliss and Manuel Kauers, Hardinian Arrays, arXiv:2309.00487 [math.CO], 2023.

Formula

Conjecture: a(n) ~ (2^4 / (3^23 * Pi^2)) * 1024^n / n^10.

Example

Example for n = 8:
  00011112
  11111122
  22222222
  22222222
  22222222
  22222222
  22222222
  22222222

Crossrefs

Cf. A253026, A253217, A252998.

Sequence in context: A051984 A232732 A228673 * A268849 A177810 A119396

Adjacent sequences: A365466 A365467 A365468 * A365470 A365471 A365472

Keyword

nonn

Author

Robert Dougherty-Bliss, Sep 04 2023

Status

approved