cp's OEIS Frontend

A252999 Number of n X 3 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 A252999 #8 Dec 08 2018 05:29:01
%S A252999 0,0,0,1,34,279,1028,2601,5318,9499,15464,23533,34026,47263,63564,
%T A252999 83249,106638,134051,165808,202229,243634,290343,342676,400953,465494,
%U A252999 536619,614648,699901,792698,893359,1002204,1119553,1245726,1381043,1525824
%N A252999 Number of n X 3 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 A252999 R. H. Hardin, <a href="/A252999/b252999.txt">Table of n, a(n) for n = 1..210</a>
%F A252999 Empirical: a(n) = (160/3)*n^3 - 708*n^2 + (9539/3)*n - 4831 for n>4.
%F A252999 Conjectures from _Colin Barker_, Dec 08 2018: (Start)
%F A252999 G.f.: x^4*(1 + 30*x + 149*x^2 + 112*x^3 + 28*x^4) / (1 - x)^4.
%F A252999 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
%F A252999 (End)
%e A252999 Some solutions for n=6:
%e A252999 ..0..0..0....0..1..1....0..1..2....0..0..1....0..0..1....0..0..1....0..1..1
%e A252999 ..0..0..1....1..1..2....1..1..2....0..1..1....0..1..1....1..1..1....1..1..2
%e A252999 ..0..0..1....1..2..2....1..1..2....0..1..2....1..1..1....1..1..1....1..1..2
%e A252999 ..1..1..1....2..2..2....1..2..2....1..1..2....1..1..2....1..1..2....1..1..2
%e A252999 ..1..1..2....2..2..2....1..2..2....1..2..2....2..2..2....1..2..2....1..2..2
%e A252999 ..2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2....2..2..2
%Y A252999 Column 3 of A253004.
%K A252999 nonn
%O A252999 1,5
%A A252999 _R. H. Hardin_, Dec 25 2014