cp's OEIS Frontend

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.

%I A253001 #8 Dec 08 2018 05:28:52
%S A253001 4,14,34,69,69,3072,39758,228484,775433,1932763,3965261,7139167,
%T A253001 11720721,17976163,26171733,36573671,49448217,65061611,83680093,
%U A253001 105569903,130997281,160228467,193529701,231167223,273407273,320516091,372759917
%N 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.
%H A253001 R. H. Hardin, <a href="/A253001/b253001.txt">Table of n, a(n) for n = 1..210</a>
%F A253001 Empirical: a(n) = (133120/3)*n^3 - 893616*n^2 + (18332582/3)*n - 14187577 for n>8.
%F A253001 Conjectures from _Colin Barker_, Dec 08 2018: (Start)
%F A253001 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.
%F A253001 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>12.
%F A253001 (End)
%e A253001 Some solutions for n=6:
%e A253001 ..0..0..0..1..2....0..0..0..1..2....0..0..0..0..1....0..0..1..1..1
%e A253001 ..1..1..1..1..2....0..1..1..1..2....0..0..1..1..1....0..0..1..1..1
%e A253001 ..1..1..2..2..2....1..1..1..1..2....0..1..1..1..1....1..1..1..2..2
%e A253001 ..1..2..2..2..2....1..1..1..1..2....1..1..1..1..2....1..1..1..2..2
%e A253001 ..1..2..2..2..2....2..2..2..2..2....1..1..1..2..2....2..2..2..2..2
%e A253001 ..2..2..2..2..2....2..2..2..2..2....2..2..2..2..2....2..2..2..2..2
%Y A253001 Column 5 of A253004.
%K A253001 nonn
%O A253001 1,1
%A A253001 _R. H. Hardin_, Dec 25 2014