A245876 Number of length 7+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

110, 2967, 12100, 40901, 97602, 214315, 404264, 727017, 1200310, 1920671, 2909100, 4309357, 6143690, 8614131, 11741392, 15797585, 20798334, 27098407, 34704020, 44065941, 55175890, 68594747, 84293880, 102959161, 124534982, 149847855

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).

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

G.f.: x*(110 + 2747*x + 5836*x^2 + 8680*x^3 + 3456*x^4 - 2178*x^5 - 1148*x^6 - 224*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).

a(n) = 1 + 37*n + 43*n^2 + 126*n^3 + 89*n^4 + 9*n^5 for n even.

a(n) = 7 - 76*n - 41*n^2 + 122*n^3 + 89*n^4 + 9*n^5 for n odd.

(End)

Example

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

Crossrefs

Row 7 of A245869.

Sequence in context: A008450 A163729 A251020 * A185536 A201833 A035836

Adjacent sequences: A245873 A245874 A245875 * A245877 A245878 A245879

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved