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A266931 Number of n X 4 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

%I A266931 #6 May 24 2021 15:03:18
%S A266931 2,5,12,35,100,288,794,2077,5110,11869,26086,54543,108999,209148,
%T A266931 386883,692473,1203061,2034487,3357115,5416951,8563297,13284702,
%U A266931 20254831,30390893,44926915,65505045,94288435,134099783,188589873,262441858
%N A266931 Number of n X 4 binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
%C A266931 Column 4 of A266935.
%H A266931 R. H. Hardin, <a href="/A266931/b266931.txt">Table of n, a(n) for n = 1..64</a>
%F A266931 Empirical: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -9*a(n-4) -a(n-5) +19*a(n-6) +13*a(n-7) -13*a(n-8) -25*a(n-9) -11*a(n-10) +15*a(n-11) +22*a(n-12) +17*a(n-13) -4*a(n-14) -23*a(n-15) -23*a(n-16) -4*a(n-17) +17*a(n-18) +22*a(n-19) +15*a(n-20) -11*a(n-21) -25*a(n-22) -13*a(n-23) +13*a(n-24) +19*a(n-25) -a(n-26) -9*a(n-27) -4*a(n-28) +3*a(n-29) +2*a(n-30) -a(n-31).
%e A266931 Some solutions for n=4
%e A266931 ..0..0..1..1....0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..1
%e A266931 ..1..1..0..1....1..1..0..0....0..0..0..1....0..0..1..0....1..1..1..0
%e A266931 ..1..1..1..0....1..1..0..1....0..0..1..0....1..1..0..0....1..1..1..0
%e A266931 ..1..1..1..1....1..1..1..0....1..1..0..0....1..1..0..0....1..1..1..0
%Y A266931 Cf. A266935.
%K A266931 nonn
%O A266931 1,1
%A A266931 _R. H. Hardin_, Jan 06 2016