A223953 Number of 6 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

64, 729, 2024, 3645, 5951, 9919, 16845, 28558, 47721, 78071, 124691, 194314, 295659, 439799, 640561, 914958, 1283653, 1771455, 2407847, 3227546, 4271095, 5585487, 7224821, 9250990, 11734401, 14754727, 18401691, 22775882, 27989603, 34167751

Offset

1,1

Comments

Row 6 of A223949.

Links

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

Formula

Empirical: a(n) = (2/45)*n^6 + (67/36)*n^4 + 8*n^3 + (7757/180)*n^2 + 138*n + 1326 for n>4.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(64 + 281*x - 1735*x^2 + 2546*x^3 - 335*x^4 - 1862*x^5 + 787*x^6 + 767*x^7 - 426*x^8 - 148*x^9 + 93*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..1..1....0..0..0....1..1..1....1..1..1....0..0..1....1..1..1....0..0..1
..0..0..0....0..0..0....0..1..1....0..1..1....0..1..1....0..0..1....0..0..1
..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..1....0..1..1
..0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1....1..1..1
..0..0..0....0..0..1....0..0..0....0..0..1....1..1..1....0..0..1....0..0..0

Crossrefs

Cf. A223949.

Sequence in context: A367803 A161860 A195249 * A224137 A016899 A250364

Adjacent sequences: A223950 A223951 A223952 * A223954 A223955 A223956

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved