A223954 Number of 7 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

128, 2187, 6869, 12856, 20275, 31899, 52532, 89135, 152495, 259230, 434069, 712692, 1145194, 1800237, 2769954, 4175669, 6174497, 8966888, 12805179, 18003218, 24947124, 34107247, 46051392, 61459371, 81138947, 106043234, 137289617

Offset

1,1

Comments

Row 7 of A223949.

Links

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

Formula

Empirical: a(n) = (4/315)*n^7 - (1/45)*n^6 + (34/45)*n^5 + (221/72)*n^4 + (4507/180)*n^3 + (42283/360)*n^2 + (53997/140)*n + 7577 for n>5.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(128 + 1163*x - 7043*x^2 + 11972*x^3 - 3753*x^4 - 9075*x^5 + 7046*x^6 + 2119*x^7 - 1755*x^8 - 2009*x^9 + 1146*x^10 + 346*x^11 - 221*x^12) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.

(End)

Example

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

Crossrefs

Cf. A223949.

Sequence in context: A195594 A321831 A351195 * A224138 A331198 A250365

Adjacent sequences: A223951 A223952 A223953 * A223955 A223956 A223957

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved