A252833 - OEIS

%I #7 Dec 06 2018 16:37:00

%S 11,53,288,1474,6068,18528,42738,79563,129173,191583,266793,354803,

%T 455613,569223,695633,834843,986853,1151663,1329273,1519683,1722893,

%U 1938903,2167713,2409323,2663733,2930943,3210953,3503763,3809373,4127783

%N 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 R. H. Hardin, <a href="/A252833/b252833.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6400*n^2 - 59190*n + 143483 for n>7.

%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)

%F 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 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

%F (End)

%e Some solutions for n=4:

%e ..0..1..1..2..2....0..1..1..2..3....0..0..1..2..3....0..1..1..2..2

%e ..0..1..1..2..3....1..1..1..2..3....1..1..1..2..3....1..1..1..2..3

%e ..1..1..2..2..3....2..2..2..2..3....1..2..2..2..3....1..1..2..2..3

%e ..1..2..2..2..3....2..3..3..3..3....1..2..2..3..3....2..2..2..3..3

%Y Column 5 of A252836.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 22 2014