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A233302 Number of (2+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..2+1} nondecreasing.

%I A233302 #17 Mar 19 2018 10:03:20
%S A233302 15,42,105,232,475,904,1632,2806,4642,7414,11500,17368,25636,37054,
%T A233302 52579,73354,100799,136586,182749,241654,316129,409430,525392,668390,
%U A233302 843514,1056524,1314050,1623542,1993496,2433398,2953979,3567152,4286297,5126192
%N A233302 Number of (2+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..2+1} nondecreasing.
%C A233302 Row 2 of A233301, row 3 of A267245.
%H A233302 R. H. Hardin, <a href="/A233302/b233302.txt">Table of n, a(n) for n = 1..172</a>
%F A233302 Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 7*a(n-3) + 10*a(n-4) + 3*a(n-5) - 6*a(n-6) - 6*a(n-7) + 3*a(n-8) + 10*a(n-9) - 7*a(n-10) - 3*a(n-11) + 4*a(n-12) - a(n-13). - _R. H. Hardin_, Jan 17 2016.
%F A233302 Empirical g.f.: x*(15 - 18*x - 18*x^2 + 43*x^3 + 6*x^4 - 30*x^5 - 21*x^6 + 22*x^7 + 33*x^8 - 31*x^9 - 8*x^10 + 15*x^11 - 4*x^12) / ((1 - x)^8*(1 + x)^3*(1 + x + x^2)). - _Colin Barker_, Mar 19 2018
%e A233302 Some solutions for n=5:
%e A233302 ..0..0..0..0..1..0....1..1..0..0..0..0....0..0..1..0..0..0....0..0..0..0..0..1
%e A233302 ..0..0..0..0..0..1....0..0..1..1..1..1....0..0..0..0..0..1....0..1..1..1..1..1
%e A233302 ..0..0..0..1..1..1....0..1..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1
%Y A233302 Cf. A233301, A267245.
%K A233302 nonn
%O A233302 1,1
%A A233302 _R. H. Hardin_, Dec 07 2013