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A245868
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Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7.
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1
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168, 712, 2368, 8840, 31176, 113024, 404264, 1455496, 5223552, 18775816, 67437448, 242306240, 870461352, 3127322696, 11235107264, 40363689352, 145010699592, 520968428032, 1871637364264, 6724074597128, 24157004951808, 86786820122120
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history;
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted derivation of recurrence
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FORMULA
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Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-3).
Empirical g.f.: 8*x*(21 + 47*x - 8*x^2) / (1 - 2*x - 6*x^2 + x^3). - Colin Barker, Nov 04 2018
Empirical recurrence verified: see link. - Robert Israel, May 13 2020
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EXAMPLE
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Some solutions for n=6:
..4....6....7....0....7....3....6....4....0....2....6....1....6....5....0....2
..2....4....6....0....2....6....3....5....7....6....0....7....6....6....7....5
..3....3....1....7....0....1....4....2....6....1....1....0....1....2....6....6
..5....6....4....4....5....6....0....6....1....1....6....1....1....1....0....1
..2....1....3....0....2....5....7....5....0....6....7....6....6....6....7....7
..4....6....4....3....4....2....2....2....7....1....0....6....7....7....2....6
..5....3....3....4....3....5....5....0....5....1....7....1....0....0....5....1
..2....4....2....3....2....4....6....5....2....6....0....2....2....6....3....7
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CROSSREFS
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Column 7 of A245869.
Sequence in context: A157998 A234823 A234816 * A251461 A110285 A302887
Adjacent sequences: A245865 A245866 A245867 * A245869 A245870 A245871
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Aug 04 2014
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STATUS
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approved
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