A245952 Number of length 2+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

26, 197, 676, 1889, 3966, 7669, 13064, 21281, 32290, 47621, 67116, 92737, 124166, 163829, 211216, 269249, 337194, 418501, 512180, 622241, 747406, 892277, 1055256, 1241569, 1449266, 1684229, 1944124, 2235521, 2555670, 2911861, 3300896, 3730817

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

Conjectures from Colin Barker, Nov 05 2018: (Start)

G.f.: x*(26 + 145*x + 230*x^2 + 299*x^3 + 18*x^4 - 141*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).

a(n) = 1 + 12*n - 5*n^2 + 18*n^3 + 3*n^4 for n even.

a(n) = 16 - 5*n - 6*n^2 + 18*n^3 + 3*n^4 for n odd.

(End)

Example

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

Crossrefs

Row 2 of A245950.

Sequence in context: A090960 A357178 A262107 * A056026 A159762 A100242

Adjacent sequences: A245949 A245950 A245951 * A245953 A245954 A245955

Keyword

nonn

Author

R. H. Hardin, Aug 08 2014

Status

approved