A202752 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

1, 4, 17, 62, 184, 462, 1022, 2052, 3819, 6688, 11143, 17810, 27482, 41146, 60012, 85544, 119493, 163932, 221293, 294406, 386540, 501446, 643402, 817260, 1028495, 1283256, 1588419, 1951642, 2381422, 2887154, 3479192, 4168912, 4968777, 5892404

Offset

1,2

Comments

Column 4 of A202756.

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (1/30)*n^5 + (5/72)*n^4 - (1/6)*n^3 + (77/180)*n^2 + (19/30)*n.

Conjectures from Colin Barker, Jun 01 2018: (Start)

G.f.: x*(1 - 3*x + 10*x^2 - 8*x^3 + 2*x^4) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=5:
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..0..1....0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..1
..0..1..1..1....0..0..1..2....0..0..0..1....0..1..2..2....0..0..1..2
..0..1..1..2....0..1..2..3....0..1..1..2....0..1..2..2....0..1..2..2

Crossrefs

Cf. A202756.

Sequence in context: A107278 A006762 A297917 * A286210 A339286 A252815

Adjacent sequences: A202749 A202750 A202751 * A202753 A202754 A202755

Keyword

nonn

Author

R. H. Hardin, Dec 23 2011

Status

approved