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A115067 a(n) = (3*n^2 - n - 2)/2. 33
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

a(n+1) is the sum of the lengths of all the segments used to draw a square of side n representing the most classic pattern for walls made of 2 X 1 bricks, known as a 1-over-2 pattern, where each joint between neighboring bricks falls over the center of the brick below. - Stefano Spezia, Jun 05 2021

LINKS

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).

FORMULA

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

E.g.f.: exp(x)*x*(8 + 3*x)/2. - Stefano Spezia, May 19 2021

EXAMPLE

Illustrations for n = 2..7 from Stefano Spezia, Jun 05 2021:

       _           _ _          _ _ _

      |_|         |_|_|        |_|_ _|

                  |_ _|        |_ _|_|

                               |_|_ _|

   a(2) = 4     a(3) = 11     a(4) = 21

    _ _ _ _     _ _ _ _ _    _ _ _ _ _ _

   |_ _|_ _|   |_ _|_ _|_|  |_ _|_ _|_ _|

   |_|_ _|_|   |_|_ _|_ _|  |_|_ _|_ _|_|

   |_ _|_ _|   |_ _|_ _|_|  |_ _|_ _|_ _|

   |_|_ _|_|   |_|_ _|_ _|  |_|_ _|_ _|_|

               |_ _|_ _|_|  |_ _|_ _|_ _|

                            |_|_ _|_ _|_|

   a(5) = 34    a(6) = 50     a(7) = 69

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

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, A095794.

Sequence in context: A038427 A323625 A301096 * A298787 A009893 A027369

Adjacent sequences:  A115064 A115065 A115066 * A115068 A115069 A115070

KEYWORD

nonn,easy,changed

AUTHOR

Roger L. Bagula, Mar 01 2006

EXTENSIONS

Edited by N. J. A. Sloane, Mar 05 2006

STATUS

approved

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Last modified June 17 18:28 EDT 2021. Contains 345085 sequences. (Running on oeis4.)