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A245875 Number of length 6+2 0..n arrays with some pair in every consecutive three terms totalling exactly n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 31 23:28 EDT 2021. Contains 346377 sequences. (Running on oeis4.)