A224042 Number of 6 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing

64, 377, 848, 1422, 2149, 3107, 4395, 6124, 8439, 11527, 15626, 21035, 28125, 37351, 49265, 64530, 83935, 108411, 139048, 177113, 224069, 281595, 351607, 436280, 538071, 659743, 804390, 975463, 1176797, 1412639, 1687677, 2007070, 2376479

Offset

1,1

Comments

Row 6 of A224038.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (35/144)*n^4 + (127/48)*n^3 + (1249/45)*n^2 + (3727/20)*n + 6 for n>4.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(64 - 71*x - 447*x^2 + 1163*x^3 - 952*x^4 + 97*x^5 + 216*x^6 - 72*x^7 + 33*x^8 - 45*x^9 + 15*x^10) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>11.

(End)

Example

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

Crossrefs

Cf. A224038.

Sequence in context: A017486 A344302 A105918 * A188840 A188703 A297343

Adjacent sequences: A224039 A224040 A224041 * A224043 A224044 A224045

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved