A245875 Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

68, 1281, 4624, 13961, 30900, 63241, 113024, 193137, 305860, 470321, 688848, 987961, 1369844, 1869561, 2488960, 3272801, 4222404, 5393377, 6786320, 8468841, 10440628, 12782441, 15492864, 18666961, 22302020, 26508561, 31282384, 36750617

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).

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

G.f.: x*(68 + 1077*x + 781*x^2 + 633*x^3 - 1143*x^4 - 561*x^5 + 103*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).

a(n) = 1 + 22*n + 31*n^2 + 77*n^3 + 29*n^4 + n^5 for n even.

a(n) = -5 - 44*n + 10*n^2 + 77*n^3 + 29*n^4 + n^5 for n odd.

(End)

Example

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

Crossrefs

Row 6 of A245869.

Sequence in context: A168179 A283575 A231060 * A329444 A230687 A337962

Adjacent sequences: A245872 A245873 A245874 * A245876 A245877 A245878

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved