A223840 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

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

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