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A245871
Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
1
10, 45, 100, 193, 318, 493, 712, 993, 1330, 1741, 2220, 2785, 3430, 4173, 5008, 5953, 7002, 8173, 9460, 10881, 12430, 14125, 15960, 17953, 20098, 22413, 24892, 27553, 30390, 33421, 36640, 40065, 43690, 47533, 51588, 55873, 60382, 65133, 70120, 75361
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
Conjectures from Colin Barker, Nov 04 2018: (Start)
G.f.: x*(10 + 15*x - 15*x^2 + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).
a(n) = 1 + 4*n + 7*n^2 + n^3 for n even.
a(n) = -2 + 4*n + 7*n^2 + n^3 for n odd.
(End)
EXAMPLE
Some solutions for n=10:
..9....1....8....0....9....0...10....4....3....5....8....4....3...10....3....9
..0....9....4....6....0...10....0....4....4....5....2....4....4....2....1....5
.10....1....6....4...10....0...10....6....6....9...10....6....6....8....9....1
.10....0....0....0....1....3....4....3....0....1....8....1....6....8....7....5
CROSSREFS
Row 2 of A245869.
Sequence in context: A238982 A292611 A275623 * A199350 A199516 A001488
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 04 2014
STATUS
approved