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A001024
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Powers of 15.
(Formerly M4990 N2147)
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35
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1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375, 576650390625, 8649755859375, 129746337890625, 1946195068359375, 29192926025390625, 437893890380859375, 6568408355712890625, 98526125335693359375, 1477891880035400390625, 22168378200531005859375, 332525673007965087890625
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OFFSET
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0,2
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COMMENTS
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Same as Pisot sequences E(1, 15), L(1, 15), P(1, 15), T(1, 15). Essentially same as Pisot sequences E(15, 225), L(15, 225), P(15, 225), T(15, 225). See A008776 for definitions of Pisot sequences.
If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4} such that for fixed y_1,y_2,...,y_n in {1,2,3,4} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan Janjic, May 24 2007
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 15-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Number of ways to assign truth values to n quaternary disjunctions connected by conjunctions such that the proposition is true. For example, a(2) = 225, since for the proposition (a v b v c v d) & (e v f v g v h) there are 225 assignments that make the proposition true. - Ori Milstein, Jan 26 2023
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: 1/(1-15x), e.g.f.: exp(15x)
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [ n eq 1 select 1 else 15*Self(n-1): n in [1..21] ];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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