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A001022
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Powers of 13.
(Formerly M4914 N2107)
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66
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1, 13, 169, 2197, 28561, 371293, 4826809, 62748517, 815730721, 10604499373, 137858491849, 1792160394037, 23298085122481, 302875106592253, 3937376385699289, 51185893014090757, 665416609183179841, 8650415919381337933, 112455406951957393129, 1461920290375446110677, 19004963774880799438801
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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, 13), L(1, 13), P(1, 13), T(1, 13). Essentially same as Pisot sequences E(13, 169), L(13, 169), P(13, 169), T(13, 169). See A008776 for definitions of Pisot sequences.
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 13-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Numbers n such that sigma(13*n) = 13*n+sigma(n). - Jahangeer Kholdi, Nov 23 2013
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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/(1-13*x).
E.g.f.: exp(13*x).
a(n) = Sum_{k=0..n} A001021(k)*binomial(n,k). It is well known that Sum_{k=0..n} (h-1)^k*binomial(n,k) = h^n. - Bruno Berselli, Aug 06 2013
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EXAMPLE
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For the fifth formula: a(7) = 1*1 + 12*7 + 144*21 + 1728*35 + 20736*35 + 248832*21 + 2985984*7 + 35831808*1 = 62748517. - Bruno Berselli, Aug 06 2013
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MAPLE
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MATHEMATICA
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PROG
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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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