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A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A001117 A353664 A353774 * A055404 A223946 A223919

Adjacent sequences:  A224146 A224147 A224148 * A224150 A224151 A224152

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 31 2013

STATUS

approved

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Last modified May 22 19:53 EDT 2022. Contains 353957 sequences. (Running on oeis4.)