cp's OEIS Frontend

A252874 Number of n X 6 nonnegative integer arrays with upper left 0 and lower right n+6-4 and value increasing by 0 or 1 with every step right or down.

%I A252874 #9 Nov 22 2015 13:19:24
%S A252874 10,120,949,5281,23203,85801,277585,806347,2142634,5281314,12207123,
%T A252874 26687363,55571337,110851465,212839721,394940091,710658874,1243696244,
%U A252874 2122211729,3538661109,5776971495,9249264713,14544867193,22494968931
%N A252874 Number of n X 6 nonnegative integer arrays with upper left 0 and lower right n+6-4 and value increasing by 0 or 1 with every step right or down.
%C A252874 Column 6 of A252876.
%H A252874 R. H. Hardin, <a href="/A252874/b252874.txt">Table of n, a(n) for n = 1..210</a>
%F A252874 Empirical: a(n) = (1/11404800)*n^12 + (1/211200)*n^11 + (37/345600)*n^10 + (143/103680)*n^9 + (27977/2419200)*n^8 + (83399/1209600)*n^7 + (318253/1036800)*n^6 + (6655/6912)*n^5 + (17647/9600)*n^4 + (350243/129600)*n^3 + (95119/277200)*n^2 + (5297/6930)*n + 3.
%F A252874 Empirical: G.f.: -x*(10 -10*x +169*x^2 -556*x^3 +1402*x^4 -2404*x^5 +2895*x^6 -2526*x^7 +1599*x^8 -716*x^9 +214*x^10 -38*x^11 +3*x^12) / (x-1)^13. - _R. J. Mathar_, Nov 21 2015
%e A252874 Some solutions for n=3:
%e A252874 ..0..1..2..2..3..3....0..1..2..3..3..4....0..1..1..2..2..3....0..0..1..2..3..4
%e A252874 ..1..2..2..3..4..4....1..2..2..3..4..4....1..1..1..2..3..4....1..1..1..2..3..4
%e A252874 ..1..2..2..3..4..5....2..2..3..4..5..5....1..1..2..3..4..5....2..2..2..3..4..5
%K A252874 nonn
%O A252874 1,1
%A A252874 _R. H. Hardin_, Dec 24 2014