A250426 Number of (n+1)X(2+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.

36, 108, 324, 720, 1600, 3000, 5625, 9450, 15876, 24696, 38416, 56448, 82944, 116640, 164025, 222750, 302500, 399300, 527076, 679536, 876096, 1107288, 1399489, 1739010, 2160900, 2646000, 3240000, 3916800, 4734976, 5659776, 6765201, 8005878

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12).

Empirical for n mod 2 = 0: a(n) = (1/256)*n^6 + (11/128)*n^5 + (49/64)*n^4 + (113/32)*n^3 + (71/8)*n^2 + (23/2)*n + 6.

Empirical for n mod 2 = 1: a(n) = (1/256)*n^6 + (11/128)*n^5 + (199/256)*n^4 + (237/64)*n^3 + (2511/256)*n^2 + (1755/128)*n + (2025/256).

a(n+1)=A202093(n). - R. J. Mathar, Dec 04 2014

Empirical g.f.: x*(36 + 36*x - 36*x^2 + 124*x^4 - 20*x^5 - 115*x^6 + 40*x^7 + 56*x^8 - 26*x^9 - 11*x^10 + 6*x^11) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Nov 14 2018

Example

Some solutions for n=6:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
..0..1..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..0....0..0..1
..0..1..1....0..0..0....0..0..1....0..0..0....0..0..1....0..1..0....0..1..1
..0..1..1....0..0..0....0..0..1....0..1..1....0..0..1....0..1..0....0..0..1
..0..1..1....0..0..0....0..0..1....0..0..1....0..1..1....0..1..0....0..1..1
..1..1..1....0..1..1....0..1..1....1..1..1....1..1..1....0..1..1....0..0..1
..0..1..1....0..1..1....0..1..1....1..0..1....1..1..1....1..1..1....1..1..1

Crossrefs

Column 2 of A250432.

Sequence in context: A282853 A341046 A162940 * A176685 A199260 A033575

Adjacent sequences: A250423 A250424 A250425 * A250427 A250428 A250429

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved