A253001 Number of n X 5 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.
4, 14, 34, 69, 69, 3072, 39758, 228484, 775433, 1932763, 3965261, 7139167, 11720721, 17976163, 26171733, 36573671, 49448217, 65061611, 83680093, 105569903, 130997281, 160228467, 193529701, 231167223, 273407273, 320516091, 372759917
Offset: 1
Keywords
Examples
Some solutions for n=6: ..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..1..1..1 ..1..1..1..1..2....0..1..1..1..2....0..0..1..1..1....0..0..1..1..1 ..1..1..2..2..2....1..1..1..1..2....0..1..1..1..1....1..1..1..2..2 ..1..2..2..2..2....1..1..1..1..2....1..1..1..1..2....1..1..1..2..2 ..1..2..2..2..2....2..2..2..2..2....1..1..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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Column 5 of A253004.
Formula
Empirical: a(n) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(4 - 2*x + 2*x^2 + x^3 - 55*x^4 + 3088*x^5 + 27642*x^6 + 87677*x^7 + 87826*x^8 + 45975*x^9 + 12629*x^10 + 1453*x^11) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.
(End)