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A223927 Number of n X 2 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing. 4
9, 54, 218, 698, 1915, 4690, 10511, 21919, 43045, 80334, 143496, 246728, 410255, 662242, 1041133, 1598477, 2402305, 3541126, 5128614, 7309062, 10263683, 14217842, 19449307, 26297611, 35174621, 46576414, 61096564, 79440948 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A223933.

LINKS

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

FORMULA

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (379/480)*n^4 + (317/144)*n^3 + (8027/2520)*n^2 + (691/420)*n + 1.

Conjectures from Colin Barker, Feb 21 2018: (Start)

G.f.: x*(9 - 27*x + 56*x^2 - 76*x^3 + 79*x^4 - 59*x^5 + 29*x^6 - 8*x^7 + x^8) / (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>9.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

CROSSREFS

Cf. A223933.

Sequence in context: A034719 A013567 A073974 * A307045 A035927 A250286

Adjacent sequences: A223924 A223925 A223926 * A223928 A223929 A223930

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 29 2013

STATUS

approved

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Last modified November 29 01:35 EST 2022. Contains 358421 sequences. (Running on oeis4.)