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

1,1

Comments

Column 1 of A204039.

Links

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

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

Example

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

Crossrefs

Cf. A204039.

Sequence in context: A258547 A211573 A211582 * A192143 A221593 A300962

Adjacent sequences: A204029 A204030 A204031 * A204033 A204034 A204035

Keyword

nonn

Author

R. H. Hardin, Jan 09 2012

Status

approved