cp's OEIS Frontend

A252833 Number of n X 5 nonnegative integer arrays with upper left 0 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 A252833 #7 Dec 06 2018 16:37:00
%S A252833 11,53,288,1474,6068,18528,42738,79563,129173,191583,266793,354803,
%T A252833 455613,569223,695633,834843,986853,1151663,1329273,1519683,1722893,
%U A252833 1938903,2167713,2409323,2663733,2930943,3210953,3503763,3809373,4127783
%N A252833 Number of n X 5 nonnegative integer arrays with upper left 0 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 A252833 R. H. Hardin, <a href="/A252833/b252833.txt">Table of n, a(n) for n = 1..210</a>
%F A252833 Empirical: a(n) = 6400*n^2 - 59190*n + 143483 for n>7.
%F A252833 Conjectures from _Colin Barker_, Dec 06 2018: (Start)
%F A252833 G.f.: x*(11 + 20*x + 162*x^2 + 758*x^3 + 2457*x^4 + 4458*x^5 + 3884*x^6 + 865*x^7+ 170*x^8 + 15*x^9) / (1 - x)^3.
%F A252833 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A252833 (End)
%e A252833 Some solutions for n=4:
%e A252833 ..0..1..1..2..2....0..1..1..2..3....0..0..1..2..3....0..1..1..2..2
%e A252833 ..0..1..1..2..3....1..1..1..2..3....1..1..1..2..3....1..1..1..2..3
%e A252833 ..1..1..2..2..3....2..2..2..2..3....1..2..2..2..3....1..1..2..2..3
%e A252833 ..1..2..2..2..3....2..3..3..3..3....1..2..2..3..3....2..2..2..3..3
%Y A252833 Column 5 of A252836.
%K A252833 nonn
%O A252833 1,1
%A A252833 _R. H. Hardin_, Dec 22 2014