A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

16, 108, 358, 884, 1928, 3902, 7490, 13784, 24467, 42053, 70195, 114073, 180875, 280385, 425693, 634043, 927836, 1335806, 1894388, 2649298, 3657346, 4988504, 6728252, 8980226, 11869193, 15544379, 20183177, 25995263, 33227149, 42167203

Offset

1,1

Comments

Row 4 of A224409.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (31/2880)*n^6 + (13/144)*n^5 + (3767/5760)*n^4 + (6409/1440)*n^3 + (189859/10080)*n^2 - (73/24)*n - 7 for n>2.

Conjectures from Colin Barker, Aug 30 2018: (Start)

G.f.: x*(16 - 36*x - 38*x^2 + 206*x^3 - 196*x^4 - 106*x^5 + 368*x^6 - 334*x^7 + 155*x^8 - 38*x^9 + 4*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..0..0....0..0..0....1..0..0....0..0..0....1..1..0....0..0..0
..0..0..1....0..0..0....1..1..0....0..1..1....1..1..0....1..1..0....1..0..0
..0..1..0....1..1..1....1..1..1....1..1..1....1..0..0....1..1..0....0..1..0
..1..0..0....1..1..1....1..1..1....1..1..0....0..1..0....1..0..0....1..0..0

Crossrefs

Cf. A224409.

Sequence in context: A297610 A083469 A224160 * A260357 A056001 A163725

Adjacent sequences: A224408 A224409 A224410 * A224412 A224413 A224414

Keyword

nonn

Author

R. H. Hardin, Apr 05 2013

Status

approved