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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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 29 2013
STATUS
approved

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Last modified June 19 18:42 EDT 2024. Contains 373507 sequences. (Running on oeis4.)