A252998 - OEIS

A252998

Number of n X n nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.

0, 0, 0, 1, 69, 3072, 122833, 4915726, 204051186, 8849413857, 399736867216, 18698541563923, 900653139548828, 44458651801451163, 2240500172425946056, 114922424191743943701, 5985232324581998309113, 315879022416448194306768

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OFFSET

1,5

COMMENTS

Diagonal of A253004.

LINKS

Robert Dougherty-Bliss and Manuel Kauers, Table of n, a(n) for n = 1..101 (first 24 terms by R. H. Hardin).

Robert Dougherty-Bliss, Experimental Methods in Number Theory and Combinatorics, Ph. D. Dissertation, Rutgers Univ. (2024). See p. 29.

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

Robert Dougherty-Bliss and Manuel Kauers, Conjectured recurrence of order 9

EXAMPLE

Some solutions for n=6:

..0..0..1..1..1..2....0..0..1..1..1..2....0..1..1..1..2..2....0..0..1..1..1..2

..0..0..1..1..1..2....0..1..1..1..2..2....1..1..1..1..2..2....0..1..1..1..1..2

..1..1..1..1..1..2....0..1..1..2..2..2....1..1..1..2..2..2....0..1..1..2..2..2

..1..1..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..1..1..2..2..2

..1..2..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..2..2..2..2..2

..2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2

CROSSREFS

Cf. A253004.

Sequence in context: A253334 A017785 A017732 * A202978 A206859 A207204

Adjacent sequences: A252995 A252996 A252997 * A252999 A253000 A253001

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved