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

16, 44, 121, 286, 676, 1482, 3249, 6840, 14400, 29640, 61009, 123994, 252004, 508526, 1026169, 2062468, 4145296, 8312988, 16670889, 33390774, 66879684, 133865682, 267944161, 536117488, 1072693504, 2145878288, 4292739361, 8586527026

Offset: 1

Author

R. H. Hardin, Jan 09 2012

Keywords

• nonn

Comments

Column 1 of A204039.

Examples

			Some solutions for n=4:
..1..0....1..1....1..1....0..1....1..1....0..0....0..0....1..0....1..1....0..0
..0..0....1..1....0..1....0..0....1..0....1..1....0..0....0..0....0..1....0..1
..0..1....1..1....1..1....1..0....1..1....0..1....1..1....0..1....1..1....1..0
..0..1....1..1....0..1....0..1....1..1....1..1....0..1....0..1....1..0....0..1
..0..1....1..1....1..1....1..1....1..1....1..1....1..1....0..1....1..1....0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A204039.

Formula

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).

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