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A252979 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.

%I A252979 #8 Dec 08 2018 04:35:45
%S A252979 3,13,33,68,1247,8487,27905,62977,114433,182273,266497,367105,484097,
%T A252979 617473,767233,933377,1115905,1314817,1530113,1761793,2009857,2274305,
%U A252979 2555137,2852353,3165953,3495937,3842305,4205057,4584193,4979713,5391617
%N A252979 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.
%H A252979 R. H. Hardin, <a href="/A252979/b252979.txt">Table of n, a(n) for n = 1..210</a>
%F A252979 Empirical: a(n) = 8192*n^2 - 87808*n + 241153 for n>6.
%F A252979 Conjectures from _Colin Barker_, Dec 08 2018: (Start)
%F A252979 G.f.: x*(3 + 4*x + 3*x^2 + 5*x^3 + 1129*x^4 + 4917*x^5 + 6117*x^6 + 3476*x^7 + 730*x^8) / (1 - x)^3.
%F A252979 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
%F A252979 (End)
%e A252979 Some solutions for n=4:
%e A252979 ..0..0..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..0
%e A252979 ..0..1..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..1..1..1
%e A252979 ..0..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1
%e A252979 ..1..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1
%Y A252979 Column 4 of A252983.
%K A252979 nonn
%O A252979 1,1
%A A252979 _R. H. Hardin_, Dec 25 2014