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A252978 Number of n X 3 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 A252978 #8 Dec 07 2018 11:39:59
%S A252978 1,1,1,33,266,851,1836,3221,5006,7191,9776,12761,16146,19931,24116,
%T A252978 28701,33686,39071,44856,51041,57626,64611,71996,79781,87966,96551,
%U A252978 105536,114921,124706,134891,145476,156461,167846,179631,191816,204401,217386
%N A252978 Number of n X 3 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 A252978 R. H. Hardin, <a href="/A252978/b252978.txt">Table of n, a(n) for n = 1..210</a>
%F A252978 Empirical: a(n) = 200*n^2 - 1615*n + 3341 for n>4.
%F A252978 Conjectures from _Colin Barker_, Dec 07 2018: (Start)
%F A252978 G.f.: x*(1 - 2*x + x^2 + 32*x^3 + 169*x^4 + 151*x^5 + 48*x^6) / (1 - x)^3.
%F A252978 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A252978 (End)
%e A252978 Some solutions for n=4:
%e A252978 ..0..0..0....0..0..0....0..0..0....0..1..1....0..0..1....0..0..0....0..0..1
%e A252978 ..0..0..0....0..0..0....0..1..1....0..1..1....0..0..1....0..0..1....0..1..1
%e A252978 ..0..1..1....0..0..1....0..1..1....0..1..1....0..0..1....0..0..1....0..1..1
%e A252978 ..1..1..1....0..0..1....1..1..1....0..1..1....0..1..1....1..1..1....0..1..1
%Y A252978 Column 3 of A252983.
%K A252978 nonn
%O A252978 1,4
%A A252978 _R. H. Hardin_, Dec 25 2014