A245874 Number of length 5+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

42, 553, 1764, 4753, 9726, 18505, 31176, 50401, 76050, 111721, 156972, 216433, 289254, 381193, 490896, 625345, 782586, 970921, 1187700, 1442641, 1732302, 2067913, 2445144, 2876833, 3357666, 3902185, 4503996, 5179441, 5920950, 6746761

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 04 2018: (Start)

G.f.: x*(42 + 469*x + 574*x^2 + 371*x^3 + 10*x^4 - 121*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).

a(n) = 1 + 12*n + 26*n^2 + 39*n^3 + 7*n^4 for n even.

a(n) = -9 - 18*n + 23*n^2 + 39*n^3 + 7*n^4 for n odd.

(End)

Example

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

Crossrefs

Row 5 of A245869.

Sequence in context: A196671 A248448 A248449 * A293096 A279888 A104901

Adjacent sequences: A245871 A245872 A245873 * A245875 A245876 A245877

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved