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

Author

R. H. Hardin, Nov 22 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 2 of A250432.

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