A245871 Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

10, 45, 100, 193, 318, 493, 712, 993, 1330, 1741, 2220, 2785, 3430, 4173, 5008, 5953, 7002, 8173, 9460, 10881, 12430, 14125, 15960, 17953, 20098, 22413, 24892, 27553, 30390, 33421, 36640, 40065, 43690, 47533, 51588, 55873, 60382, 65133, 70120, 75361

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).

Conjectures from Colin Barker, Nov 04 2018: (Start)

G.f.: x*(10 + 15*x - 15*x^2 + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = 1 + 4*n + 7*n^2 + n^3 for n even.

a(n) = -2 + 4*n + 7*n^2 + n^3 for n odd.

(End)

Example

Some solutions for n=10:
..9....1....8....0....9....0...10....4....3....5....8....4....3...10....3....9
..0....9....4....6....0...10....0....4....4....5....2....4....4....2....1....5
.10....1....6....4...10....0...10....6....6....9...10....6....6....8....9....1
.10....0....0....0....1....3....4....3....0....1....8....1....6....8....7....5

Crossrefs

Row 2 of A245869.

Sequence in context: A238982 A292611 A275623 * A199350 A199516 A001488

Adjacent sequences: A245868 A245869 A245870 * A245872 A245873 A245874

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved