A223952 Number of 5 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

32, 243, 596, 1062, 1821, 3115, 5233, 8564, 13613, 21017, 31561, 46194, 66045, 92439, 126913, 171232, 227405, 297701, 384665, 491134, 620253, 775491, 960657, 1179916, 1437805, 1739249, 2089577, 2494538, 2960317, 3493551, 4101345, 4791288, 5571469

Offset

1,1

Comments

Row 5 of A223949.

Links

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

Formula

Empirical: a(n) = (2/15)*n^5 + (1/6)*n^4 + (23/6)*n^3 + (89/6)*n^2 + (1501/30)*n + 200 for n>3.

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

G.f.: x*(32 + 51*x - 382*x^2 + 491*x^3 + 9*x^4 - 348*x^5 + 132*x^6 + 68*x^7 - 37*x^8) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.

(End)

Example

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

Crossrefs

Cf. A223949.

Sequence in context: A111442 A104782 A186774 * A224136 A250363 A346637

Adjacent sequences: A223949 A223950 A223951 * A223953 A223954 A223955

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved