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A223840 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
5, 25, 89, 249, 596, 1286, 2578, 4886, 8851, 15439, 26072, 42800, 68523, 107273, 164567, 247843, 366992, 535000, 768715, 1089755, 1525574, 2110704, 2888192, 3911252, 5245153, 6969365, 9179986, 11992474, 15544709, 20000411, 25552941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 4 of A223838.

LINKS

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

FORMULA

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (19/2880)*n^6 + (7/180)*n^5 + (527/5760)*n^4 + (3683/1440)*n^3 + (4051/10080)*n^2 - (1707/280)*n + 13 for n>2.

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

G.f.: x*(5 - 20*x + 44*x^2 - 72*x^3 + 89*x^4 - 70*x^5 + 28*x^6 - 4*x^7 + 4*x^8 - 4*x^9 + x^10) / (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>11.

(End)

EXAMPLE

Some solutions for n=3:

..0..0..0....0..1..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..0

..0..0..0....0..1..0....0..0..0....0..1..1....0..0..0....0..0..1....0..0..0

..0..0..0....0..1..0....1..0..0....1..1..1....0..0..0....0..0..1....0..1..0

..0..0..1....1..1..1....1..1..0....1..1..1....0..1..1....0..1..1....0..1..0

CROSSREFS

Cf. A223838.

Sequence in context: A147274 A147034 A146460 * A083090 A224148 A265929

Adjacent sequences:  A223837 A223838 A223839 * A223841 A223842 A223843

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2013

STATUS

approved

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Last modified May 18 18:42 EDT 2022. Contains 353824 sequences. (Running on oeis4.)