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A266429 Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

%I A266429 #8 Jan 09 2019 14:45:27
%S A266429 4,13,39,106,259,574,1170,2223,3982,6787,11089,17472,26677,39628,
%T A266429 57460,81549,113544,155401,209419,278278,365079,473386,607270,771355,
%U A266429 970866,1211679,1500373,1844284,2251561,2731224,3293224,3948505,4709068,5588037
%N A266429 Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
%H A266429 R. H. Hardin, <a href="/A266429/b266429.txt">Table of n, a(n) for n = 1..210</a>
%F A266429 Empirical: a(n) = (1/360)*n^6 + (1/40)*n^5 + (1/9)*n^4 + (7/24)*n^3 + (319/360)*n^2 + (101/60)*n + 1.
%F A266429 Conjectures from _Colin Barker_, Jan 09 2019: (Start)
%F A266429 G.f.: x*(4 - 15*x + 32*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A266429 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A266429 (End)
%e A266429 Some solutions for n=4:
%e A266429 ..0..0..0..1....0..1..1..1....0..0..0..1....0..0..1..1....0..0..0..0
%e A266429 ..0..0..1..0....0..1..1..1....0..0..0..1....0..0..1..1....0..0..1..1
%e A266429 ..0..0..1..1....1..0..0..1....0..0..0..1....0..1..1..1....1..1..0..0
%Y A266429 Row 3 of A266428.
%K A266429 nonn
%O A266429 1,1
%A A266429 _R. H. Hardin_, Dec 29 2015