A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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

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