A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

6, 36, 155, 526, 1509, 3827, 8838, 18969, 38392, 74053, 137204, 245636, 426869, 722624, 1194983, 1934737, 3072530, 4793530, 7356497, 11118274, 16564901, 24350745, 35347252, 50703161, 71918276, 100933171, 140237506, 192999960

Offset

1,1

Comments

Row 5 of A224146.

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 + (11/120960)*n^8 + (59/40320)*n^7 + (3853/172800)*n^6 + (181/1280)*n^5 + (100381/181440)*n^4 + (76319/60480)*n^3 + (24247/12600)*n^2 + (23/21)*n + 1.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(6 - 30*x + 89*x^2 - 189*x^3 + 288*x^4 - 309*x^5 + 236*x^6 - 127*x^7 + 46*x^8 - 10*x^9 + x^10) / (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>11.

(End)

Example

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

Crossrefs

Cf. A224146.

Sequence in context: A357087 A357025 A357085 * A055404 A223946 A223919

Adjacent sequences: A224146 A224147 A224148 * A224150 A224151 A224152

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved