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A245876 Number of length 7+2 0..n arrays with some pair in every consecutive three terms totalling exactly n. 1
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 (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) = 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

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Last modified September 20 12:13 EDT 2020. Contains 337264 sequences. (Running on oeis4.)