A250727 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

579, 1376, 2699, 4889, 8514, 14437, 23941, 38821, 61554, 95438, 144820, 215289, 313964, 449751, 633699, 879329, 1203066, 1624648, 2167642, 2859941, 3734372, 4829289, 6189281, 7865869, 9918322, 12414466, 15431616, 19057505, 23391340

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 20*a(n-2) + 28*a(n-3) - 14*a(n-4) - 14*a(n-5) + 28*a(n-6) - 20*a(n-7) + 7*a(n-8) - a(n-9) for n>14.

Empirical for n mod 2 = 0: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (179/720)*n^5 + (427/144)*n^4 + (4559/720)*n^3 + (41227/360)*n^2 + (81253/210)*n + 25 for n>5.

Empirical for n mod 2 = 1: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (179/720)*n^5 + (427/144)*n^4 + (4559/720)*n^3 + (41227/360)*n^2 + (81253/210)*n + 27 for n>5.

Empirical g.f.: x*(579 - 2677*x + 4647*x^2 - 2696*x^3 - 2151*x^4 + 4417*x^5 - 2892*x^6 + 866*x^7 - 72*x^8 - 19*x^9 + 9*x^10 - 15*x^11 + 10*x^12 - 2*x^13) / ((1 - x)^8*(1 + x)). - Colin Barker, Nov 16 2018

Example

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

Crossrefs

Column 6 of A250729.

Sequence in context: A097768 A286233 A073735 * A252985 A097769 A186786

Adjacent sequences: A250724 A250725 A250726 * A250728 A250729 A250730

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved