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A115067
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a(n) = (3*n^2 - n - 2)/2.
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31
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0, 4, 11, 21, 34, 50, 69, 91, 116, 144, 175, 209, 246, 286, 329, 375, 424, 476, 531, 589, 650, 714, 781, 851, 924, 1000, 1079, 1161, 1246, 1334, 1425, 1519, 1616, 1716, 1819, 1925, 2034, 2146, 2261, 2379, 2500, 2624, 2751, 2881, 3014, 3150, 3289, 3431, 3576
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OFFSET
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1,2
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COMMENTS
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Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative integer lattice point of the orbit, when the cardinality of the orbit is equal to 6720. - Philippe A.J.G. Chevalier, Dec 28 2015
a(n) = the sum of the numerator and denominator of the reduced fraction resulting from the sum A000217(n-2)/A000217(n-1) + A000217(n-1)/A000217(n), n>1. - J. M. Bergot, Jun 10 2017
For n > 1, a(n) is also the number of (not necessarily maximum) cliques in the (n-1)-Andrasfai graph. - Eric W. Weisstein, Nov 29 2017
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Alfred Hoehn, Illustration of initial terms of A000326, A005449, A045943, A115067
Eric Weisstein's World of Mathematics, Andrasfai Graph
Eric Weisstein's World of Mathematics, Clique
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = (3*n+2)*(n-1)/2.
a(n+1) = n*(3*n + 5)/2. - Omar E. Pol, May 21 2008
a(n) = 3*n + a(n-1) - 2 for n>1, a(1)=0. - Vincenzo Librandi, Nov 13 2010
a(n) = A095794(-n). - Bruno Berselli, Sep 02 2011
G.f.: x^2*(4-x) / (1-x)^3. - R. J. Mathar, Sep 02 2011
a(n) = A055998(2*n-2) - A055998(n-1). - Bruno Berselli, Sep 23 2016
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MATHEMATICA
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Table[n (3 n - 1)/2 - 1, {n, 50}] (* Vincenzo Librandi, Jun 11 2017 *)
LinearRecurrence[{3, -3, 1}, {0, 4, 11}, 20] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(-4 + x) x/(-1 + x)^3, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)
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PROG
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(PARI) a(n)=n*(3*n-1)/2-1 \\ Charles R Greathouse IV, Jan 27 2012
(MAGMA) [n*(3*n-1)/2-1: n in [1..50]]; // Vincenzo Librandi, Jun 11 2017
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CROSSREFS
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The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.
Orbits of Aut(Z^7) as function of the infinity norm A000579, A154286, A102860, A002412, A045943, A008585, A005843, A001477, A000217.
Cf. A055998.
Sequence in context: A016438 A038427 A301096 * A298787 A009893 A027369
Adjacent sequences: A115064 A115065 A115066 * A115068 A115069 A115070
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula, Mar 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Mar 05 2006
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STATUS
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approved
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