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A223756 Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal. 5
16, 256, 2500, 16900, 87616, 372100, 1352569, 4338889, 12559936, 33362176, 82373776, 190992400, 419266576, 877225924, 1759047481, 3396208729, 6338070544, 11471266816, 20192978404, 34657779556, 58123423744, 95427859396 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A223762.

LINKS

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

FORMULA

Empirical: a(n) = (1/518400)*n^12 + (1/17280)*n^11 + (91/103680)*n^10 + (71/8640)*n^9 + (9101/172800)*n^8 + (457/1920)*n^7 + (81397/103680)*n^6 + (497/270)*n^5 + (203687/64800)*n^4 + (1933/540)*n^3 + (2533/720)*n^2 + (11/6)*n + 1.

a(n) = A223659(n)^2. - Mark van Hoeij, May 14 2013

Conjectures from Colin Barker, Feb 19 2018: (Start)

G.f.: x*(16 + 48*x + 420*x^2 - 208*x^3 + 1140*x^4 - 1260*x^5 + 1401*x^6 - 1044*x^7 + 597*x^8 - 244*x^9 + 69*x^10 - 12*x^11 + x^12) / (1 - x)^13.

a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.

(End)

EXAMPLE

Some solutions for n=3:

..3..2....0..0....0..0....1..2....0..3....2..1....1..3....0..0....3..1....3..1

..2..0....1..1....1..2....3..2....1..3....2..3....3..3....0..0....1..0....2..3

..2..0....3..0....1..2....0..0....2..1....1..3....3..2....0..3....1..0....0..3

CROSSREFS

Sequence in context: A189191 A188876 A223634 * A188905 A189106 A189112

Adjacent sequences:  A223753 A223754 A223755 * A223757 A223758 A223759

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2013

STATUS

approved

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)