A224160 Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

16, 108, 281, 574, 1156, 2271, 4339, 8008, 14257, 24519, 40840, 66082, 104179, 160456, 242022, 358249, 521350, 747070, 1055505, 1472065, 2028598, 2764693, 3729181, 4981854, 6595423, 8657737, 11274286, 14571012, 18697453, 23830246

Offset

1,1

Comments

Row 4 of A224158.

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 + (31/2880)*n^6 + (43/720)*n^5 + (3527/5760)*n^4 - (5947/1440)*n^3 + (548119/10080)*n^2 - (119221/840)*n + 283 for n>4.

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

G.f.: x*(16 - 36*x - 115*x^2 + 589*x^3 - 950*x^4 + 519*x^5 + 442*x^6 - 977*x^7 + 817*x^8 - 436*x^9 + 178*x^10 - 55*x^11 + 9*x^12) / (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>13.

(End)

Example

Some solutions for n=3:
..1..1..0....1..1..0....1..1..0....0..0..0....1..1..1....0..0..1....0..0..1
..1..1..0....1..1..1....1..1..1....0..0..0....1..1..1....0..1..0....0..1..1
..1..1..0....1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....1..1..0
..1..0..0....1..1..0....1..1..0....1..1..1....1..1..0....1..1..1....1..1..0

Crossrefs

Cf. A224158.

Sequence in context: A097762 A297610 A083469 * A224411 A260357 A056001

Adjacent sequences: A224157 A224158 A224159 * A224161 A224162 A224163

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved