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A223914 Number of n X 4 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
46, 548, 3311, 14123, 48182, 139925, 359344, 837243, 1802306, 3633256, 6929795, 12606425, 22013660, 37091549, 60560840, 96157525, 148916916, 225513812, 334665727, 487606559, 698638490, 985770317, 1371450824, 1883406215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A223918.

LINKS

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

FORMULA

Empirical: a(n) = (41/4032)*n^8 + (41/336)*n^7 + (1277/1440)*n^6 + (953/240)*n^5 + (5363/576)*n^4 + (35/2)*n^3 + (28211/1680)*n^2 - (223/140)*n - 7 for n>1.

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

G.f.: x*(46 + 134*x + 35*x^2 + 188*x^3 + 35*x^4 - 157*x^5 + 241*x^6 - 153*x^7 + 47*x^8 - 6*x^9) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

CROSSREFS

Cf. A223918.

Sequence in context: A232071 A156892 A224258 * A224186 A027940 A098227

Adjacent sequences:  A223911 A223912 A223913 * A223915 A223916 A223917

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 29 2013

STATUS

approved

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Last modified September 30 13:02 EDT 2022. Contains 357105 sequences. (Running on oeis4.)