cp's OEIS Frontend

A253221 Number of n X 6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 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 A253221 #13 Dec 12 2018 09:39:55
%S A253221 10,49,263,1249,3568,3568,47698,213155,538444,1039060,1719174,2579462,
%T A253221 3619974,4840710,6241670,7822854,9584262,11525894,13647750,15949830,
%U A253221 18432134,21094662,23937414,26960390,30163590,33547014,37110662,40854534
%N A253221 Number of n X 6 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 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 A253221 R. H. Hardin, <a href="/A253221/b253221.txt">Table of n, a(n) for n = 1..210</a>
%F A253221 Empirical: a(n) = 90112*n^2 - 1212288*n + 4150790 for n > 10.
%F A253221 Conjectures from _Colin Barker_, Dec 10 2018: (Start)
%F A253221 G.f.: x*(10 + 19*x + 146*x^2 + 597*x^3 + 561*x^4 - 3652*x^5 + 46449*x^6 + 77197*x^7 + 38505*x^8 + 15495*x^9 + 4171*x^10 + 676*x^11 + 50*x^12) / (1 - x)^3.
%F A253221 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 13.
%F A253221 (End)
%e A253221 Some solutions for n=4:
%e A253221   0 0 1 2 2 3    0 0 0 1 2 3    0 1 1 2 2 3    0 0 1 2 2 3
%e A253221   1 1 1 2 2 3    0 1 1 1 2 3    1 1 1 2 3 3    0 1 1 2 2 3
%e A253221   1 1 1 2 2 3    1 1 2 2 2 3    2 2 2 2 3 3    0 1 2 2 3 3
%e A253221   2 2 2 2 3 3    2 2 2 3 3 3    2 3 3 3 3 3    1 1 2 3 3 3
%Y A253221 Column 6 of A253223.
%K A253221 nonn
%O A253221 1,1
%A A253221 _R. H. Hardin_, Dec 29 2014