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A204032 Number of (n+1) X 2 0..1 arrays with the sums of 2 X 2 subblocks nondecreasing rightwards and downwards. 4

%I

%S 16,44,121,286,676,1482,3249,6840,14400,29640,61009,123994,252004,

%T 508526,1026169,2062468,4145296,8312988,16670889,33390774,66879684,

%U 133865682,267944161,536117488,1072693504,2145878288,4292739361,8586527026

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

%C Column 1 of A204039.

%H R. H. Hardin, <a href="/A204032/b204032.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=4:

%e ..1..0....1..1....1..1....0..1....1..1....0..0....0..0....1..0....1..1....0..0

%e ..0..0....1..1....0..1....0..0....1..0....1..1....0..0....0..0....0..1....0..1

%e ..0..1....1..1....1..1....1..0....1..1....0..1....1..1....0..1....1..1....1..0

%e ..0..1....1..1....0..1....0..1....1..1....1..1....0..1....0..1....1..0....0..1

%e ..0..1....1..1....1..1....1..1....1..1....1..1....1..1....0..1....1..1....0..1

%Y Cf. A204039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 09 2012

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)