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A008594 Multiples of 12. 31
0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 36 ).

The positive terms are the differences of consecutive star numbers (A003154). - Mihir Mathur, Jun 07 2013

A089911(a(n)) = 0. - Reinhard Zumkeller, Jul 05 2013

a(1) = 12 is a primitive abundant number, thus all a(n), n >= 2, are nonprimitive abundant numbers. - Daniel Forgues, Sep 24 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Tanya Khovanova, Recursive Sequences

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 324

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))

William A. Stein, The modular forms database

Wikipedia, Star Number

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = 12*n. a(n) = 2*a(n-1)-a(n-2) for n>1. G.f.: 12*x/(1-x)^2. - Vincenzo Librandi, Jun 11 2011

a(n) = A003154(n)- A003154(n-1). - Mihir Mathur, Jun 07 2013

MAPLE

A008594:=n->12*n: seq(A008594(n), n=0..100); # Wesley Ivan Hurt, Sep 24 2016

MATHEMATICA

12*Range[0, 200] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

PROG

(MAGMA) [12*n: n in [0..50]]; // Vincenzo Librandi, Jun 11 2011

(Haskell)

a008594 = (* 12)

a008594_list = [0, 12 ..]  -- Reinhard Zumkeller, Dec 12 2012

(PARI) a(n)=12*n \\ Charles R Greathouse IV, Apr 21 2015

CROSSREFS

Subsequence of A072065 and A121032.

Cf. A008592, A008593, A003154.

Sequence in context: A044852 A121578 A044897 * A033024 A044837 A033009

Adjacent sequences:  A008591 A008592 A008593 * A008595 A008596 A008597

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 27 00:46 EDT 2017. Contains 285506 sequences.