A008594 Multiples of 12.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Subsequence of A072065 and A121032.

Cf. A003154, A008588, A008592, A008593, A008606, A089911.

Programs

Haskell

a008594 = (* 12)
a008594_list = [0, 12 ..]  -- Reinhard Zumkeller, Dec 12 2012

Magma

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

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 *)

PARI

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

Formula

From Vincenzo Librandi, Jun 11 2011: (Start)

a(n) = 12*n.

a(n) = 2*a(n-1) - a(n-2) for n > 1.

G.f.: 12*x/(1-x)^2. (End)

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

From Elmo R. Oliveira, Apr 10 2025: (Start)

E.g.f.: 12*x*exp(x).

a(n) = 2*A008588(n) = A008606(n)/2. (End)