A223945 Number of n X 4 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

5, 25, 96, 321, 1062, 3645, 12856, 45626, 161604, 571202, 2018635, 7138542, 25257472, 89382635, 316317650, 1119405165, 3961434035, 14019204346, 49613421418, 175580918227, 621378416037, 2199050475783, 7782414885011

Offset

1,1

Comments

Column 4 of A223949.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 5*a(n-2) - 2*a(n-3) + 7*a(n-4) - 2*a(n-5) - 4*a(n-6) - 61*a(n-7) + 29*a(n-8) + 8*a(n-9) + 8*a(n-10).

Empirical g.f.: x*(5 - 4*x^2 - 24*x^3 - 48*x^4 - 33*x^5 - 19*x^6 + 45*x^7 + 16*x^8 + 8*x^9) / (1 - 5*x + 5*x^2 + 2*x^3 - 7*x^4 + 2*x^5 + 4*x^6 + 61*x^7 - 29*x^8 - 8*x^9 - 8*x^10). - Colin Barker, Aug 24 2018

Example

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

Crossrefs

Cf. A223949.

Sequence in context: A126878 A203340 A055343 * A197085 A273747 A201841

Adjacent sequences: A223942 A223943 A223944 * A223946 A223947 A223948

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved