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 A054621 Number of ways to color vertices of a 7-gon using <= n colors, allowing only rotations. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Length-7 necklaces with n kinds of beads. -Vincenzo Librandi Apr 30 2012 LINKS 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). FORMULA 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Row 7 of A075195. Cf. A054622. Sequence in context: A006300 A034094 A011197 * A111778 A024387 A101310 Adjacent sequences:  A054618 A054619 A054620 * A054622 A054623 A054624 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 16 2000 EXTENSIONS Edited by Christian G. Bower, Sep 07 2002 STATUS approved

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