A008594 Multiples of 12: a(n) = 12*n.

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

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 *)
NestList[12+#&, 0, 60] (* Harvey P. Dale, Feb 02 2022 *)

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

Author

N. J. A. Sloane

Status

approved