cp's OEIS Frontend

A253000 Number of n X 4 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 A253000 #8 Dec 08 2018 05:28:56
%S A253000 1,1,1,1,69,1132,7235,25233,63135,129133,231419,378185,577623,837925,
%T A253000 1167283,1573889,2065935,2651613,3339115,4136633,5052359,6094485,
%U A253000 7271203,8590705,10061183,11690829,13487835,15460393,17616695,19964933,22513299
%N A253000 Number of n X 4 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 A253000 R. H. Hardin, <a href="/A253000/b253000.txt">Table of n, a(n) for n = 1..210</a>
%F A253000 Empirical: a(n) = (4096/3)*n^3 - 22816*n^2 + (388490/3)*n - 249567 for n>6.
%F A253000 Conjectures from _Colin Barker_, Dec 08 2018: (Start)
%F A253000 G.f.: x*(1 - 3*x + 3*x^2 - x^3 + 68*x^4 + 859*x^5 + 3118*x^6 + 2810*x^7 + 1154*x^8 + 183*x^9) / (1 - x)^4.
%F A253000 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
%F A253000 (End)
%e A253000 Some solutions for n=6:
%e A253000 ..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..1..2
%e A253000 ..0..0..0..1....1..1..1..1....0..1..1..1....0..1..1..1....1..1..1..2
%e A253000 ..0..1..1..1....1..1..2..2....1..1..1..2....1..1..2..2....1..1..1..2
%e A253000 ..0..1..2..2....1..1..2..2....2..2..2..2....1..2..2..2....1..1..1..2
%e A253000 ..1..1..2..2....1..2..2..2....2..2..2..2....1..2..2..2....1..1..1..2
%e A253000 ..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2
%Y A253000 Column 4 of A253004.
%K A253000 nonn
%O A253000 1,5
%A A253000 _R. H. Hardin_, Dec 25 2014