A253228 Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

907, 1775, 1709, 2543, 3936, 6414, 11022, 19851, 37083, 71082, 138576, 273021, 541329, 1077324, 2148654, 4290615, 8573799, 17139390, 34269756, 68529633, 137048493, 274085280, 548157882, 1096302075, 2192589411, 4385162994

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

Conjectures from Colin Barker, Dec 10 2018: (Start)

G.f.: x*(907 - 2760*x + 997*x^2 + 3624*x^3 - 4009*x^4 + 1208*x^5 - 7*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

a(n) = (3/32)*(5280 + 697*2^n + 1840*n + 208*n^2) for n>4.

(End)

Example

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

Crossrefs

Column 5 of A253231.

Sequence in context: A195987 A216468 A031939 * A134075 A316679 A177998

Adjacent sequences: A253225 A253226 A253227 * A253229 A253230 A253231

Keyword

nonn

Author

R. H. Hardin, Dec 29 2014

Status

approved