cp's OEIS Frontend

A204032 Number of (n+1) X 2 0..1 arrays with the sums of 2 X 2 subblocks nondecreasing rightwards and downwards.

%I A204032 #11 Feb 20 2018 07:38:37
%S A204032 16,44,121,286,676,1482,3249,6840,14400,29640,61009,123994,252004,
%T A204032 508526,1026169,2062468,4145296,8312988,16670889,33390774,66879684,
%U A204032 133865682,267944161,536117488,1072693504,2145878288,4292739361,8586527026
%N A204032 Number of (n+1) X 2 0..1 arrays with the sums of 2 X 2 subblocks nondecreasing rightwards and downwards.
%C A204032 Column 1 of A204039.
%H A204032 R. H. Hardin, <a href="/A204032/b204032.txt">Table of n, a(n) for n = 1..210</a>
%F A204032 Empirical: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9).
%F A204032 Empirical g.f.: x*(16 - 20*x - 55*x^2 + 90*x^3 + 52*x^4 - 144*x^5 + 20*x^6 + 72*x^7 - 32*x^8) / ((1 - x)^3*(1 + x)*(1 - 2*x)*(1 - 2*x^2)^2). - _Colin Barker_, Feb 20 2018
%e A204032 Some solutions for n=4:
%e A204032 ..1..0....1..1....1..1....0..1....1..1....0..0....0..0....1..0....1..1....0..0
%e A204032 ..0..0....1..1....0..1....0..0....1..0....1..1....0..0....0..0....0..1....0..1
%e A204032 ..0..1....1..1....1..1....1..0....1..1....0..1....1..1....0..1....1..1....1..0
%e A204032 ..0..1....1..1....0..1....0..1....1..1....1..1....0..1....0..1....1..0....0..1
%e A204032 ..0..1....1..1....1..1....1..1....1..1....1..1....1..1....0..1....1..1....0..1
%Y A204032 Cf. A204039.
%K A204032 nonn
%O A204032 1,1
%A A204032 _R. H. Hardin_, Jan 09 2012