A223774 Number of n X 5 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

16, 101, 371, 1040, 2516, 5573, 11635, 23230, 44703, 83305, 150815, 265901, 457485, 769447, 1267085, 2045843, 3242928, 5052561, 7745747, 11695606, 17409482, 25569241, 37081383, 53138828, 75296493, 105563057, 146511615, 201412251

Offset

1,1

Comments

Column 5 of A223777.

Links

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

Formula

Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (1/8640)*n^8 + (11/8064)*n^7 + (4273/172800)*n^6 + (589/11520)*n^5 + (649763/362880)*n^4 + (589/12096)*n^3 + (102443/2400)*n^2 - (16061/168)*n + 93 for n>2.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(16 - 75*x + 140*x^2 - 126*x^3 + 96*x^4 - 180*x^5 + 272*x^6 - 200*x^7 + 65*x^8 - 20*x^9 + 27*x^10 - 18*x^11 + 4*x^12) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>13.

(End)

Example

Some solutions for n=3:
..0..0..0..0..0....1..0..0..0..0....1..0..0..0..0....0..0..0..0..0
..1..0..0..0..0....1..0..0..0..0....0..0..0..0..1....0..0..0..0..0
..0..0..0..0..1....0..0..1..1..1....0..0..0..1..0....0..0..1..1..0

Crossrefs

Cf. A223777.

Sequence in context: A061432 A115328 A223767 * A224155 A224406 A223016

Adjacent sequences: A223771 A223772 A223773 * A223775 A223776 A223777

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved