cp's OEIS Frontend

A266430 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

%I A266430 #8 Jan 09 2019 21:23:31
%S A266430 5,22,96,404,1556,5365,16585,46463,119452,285124,638247,1351194,
%T A266430 2724385,5262379,9785590,17590461,30674359,52045522,86143170,
%U A266430 139398464,220973442,343722465,525429159,790381435,1171358006,1712112000,2470450897
%N A266430 Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
%H A266430 R. H. Hardin, <a href="/A266430/b266430.txt">Table of n, a(n) for n = 1..210</a>
%F A266430 Empirical: a(n) = (1/9979200)*n^11 + (1/201600)*n^10 + (1/12096)*n^9 + (1/1344)*n^8 + (1271/302400)*n^7 + (479/28800)*n^6 + (12797/181440)*n^5 + (97/504)*n^4 + (1779/2800)*n^3 + (2032/1575)*n^2 + (8269/4620)*n + 1.
%F A266430 Conjectures from _Colin Barker_, Jan 09 2019: (Start)
%F A266430 G.f.: x*(5 - 38*x + 162*x^2 - 396*x^3 + 679*x^4 - 833*x^5 + 737*x^6 - 471*x^7 + 213*x^8 - 65*x^9 + 12*x^10 - x^11) / (1 - x)^12.
%F A266430 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
%F A266430 (End)
%e A266430 Some solutions for n=4:
%e A266430 ..0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1
%e A266430 ..0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1
%e A266430 ..0..1..0..1....0..1..1..1....0..0..1..1....1..1..0..1....0..1..1..1
%e A266430 ..1..0..0..1....1..0..0..0....0..0..1..1....1..1..1..1....1..1..0..1
%Y A266430 Row 4 of A266428.
%K A266430 nonn
%O A266430 1,1
%A A266430 _R. H. Hardin_, Dec 29 2015