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A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing. 1
81, 1296, 5880, 19608, 57387, 151010, 363392, 810436, 1693423, 3344982, 6292120, 11340202, 19682181, 33037788, 53827802, 85388930, 132235237, 200372476, 297672078, 434311972, 623291815, 881030622, 1228055196, 1689788168 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 4 of A224353.

LINKS

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

FORMULA

Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (239/288)*n^6 + (109/24)*n^5 + (12079/576)*n^4 + (39/16)*n^3 + (310151/1008)*n^2 - (21299/84)*n + 142 for n>3.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(81 + 567*x - 2868*x^2 + 6540*x^3 - 6063*x^4 - 415*x^5 + 7550*x^6 - 8564*x^7 + 4918*x^8 - 1584*x^9 + 262*x^10 - 14*x^11) / (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>12.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Cf. A224353.

Sequence in context: A231994 A236790 A232876 * A016768 A224014 A059977

Adjacent sequences:  A224352 A224353 A224354 * A224356 A224357 A224358

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 04 2013

STATUS

approved

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)