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A054621
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Number of ways to color vertices of a 7-gon using <= n colors, allowing only rotations.
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4
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0, 1, 20, 315, 2344, 11165, 39996, 117655, 299600, 683289, 1428580, 2783891, 5118840, 8964085, 15059084, 24408495, 38347936, 58619825, 87460020, 127695979, 182857160, 257298381, 356336860, 486403655, 655210224, 871930825, 1147401476
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OFFSET
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0,3
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COMMENTS
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Length-7 necklaces with n kinds of beads. -Vincenzo Librandi Apr 30 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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a(n) = sum_{d|7} phi(d)*n^(7/d)/7 = n^7/7 +7*n/6.
G.f. x*(1+12*x+183*x^2+328*x^3+183*x^4+12*x^5+x^6) / (x-1)^8 . - R. J. Mathar, Aug 30 2011
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MATHEMATICA
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CoefficientList[Series[x*(1+12*x+183*x^2+328*x^3+183*x^4+ 12*x^5+x^6)/(x-1)^8, {x, 0, 33}], x] (* Vincenzo Librandi Apr 30 2012 *)
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PROG
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(MAGMA) I:=[0, 1, 20, 315, 2344, 11165, 39996, 117655]; [n le 8 select I[n] else 8*Self(n-1)-28*Self(n-2)+56*Self(n-3)-70*Self(n-4)+56*Self(n-5)-28*Self(n-6)+8*Self(n-7)-Self(n-8): n in [1..30]]; // Vincenzo Librandi Apr 30 2012
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CROSSREFS
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Row 7 of A075195. Cf. A054622.
Sequence in context: A006300 A034094 A011197 * A111778 A024387 A101310
Adjacent sequences: A054618 A054619 A054620 * A054622 A054623 A054624
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Apr 16 2000
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EXTENSIONS
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Edited by Christian G. Bower, Sep 07 2002
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STATUS
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approved
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