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A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1
5, 25, 92, 272, 691, 1573, 3296, 6472, 12058, 21506, 36961, 61517, 99542, 157084, 242371, 366419, 543763, 793327, 1139450, 1613086, 2253197, 3108359, 4238602, 5717506, 7634576, 10097920, 13237255, 17207267, 22191352, 28405766, 36104213 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 4 of A224146.

LINKS

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

FORMULA

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (1/192)*n^6 + (1/16)*n^5 + (223/640)*n^4 + (149/160)*n^3 + (3319/2016)*n^2 + (169/168)*n + 1.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(5 - 20*x + 47*x^2 - 76*x^3 + 85*x^4 - 62*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:

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

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

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

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

CROSSREFS

Cf. A224146.

Sequence in context: A146460 A223840 A083090 * A265929 A297452 A147177

Adjacent sequences:  A224145 A224146 A224147 * A224149 A224150 A224151

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 31 2013

STATUS

approved

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Last modified October 16 05:38 EDT 2019. Contains 328044 sequences. (Running on oeis4.)