A047233 Numbers that are congruent to {0, 4} mod 6.

0, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 58, 60, 64, 66, 70, 72, 76, 78, 82, 84, 88, 90, 94, 96, 100, 102, 106, 108, 112, 114, 118, 120, 124, 126, 130, 132, 136, 138, 142, 144, 148, 150, 154, 156, 160, 162, 166, 168, 172, 174, 178, 180, 184, 186, 190, 192, 196, 198

Offset

1,2

Comments

Apart from initial term(s), dimension of the space of weight 2*n cusp forms for Gamma_0(17).

Nonnegative k such that k*(k + 2)/6 is an integer. - Bruno Berselli, Mar 06 2018

Links

Bruno Berselli, Table of n, a(n) for n = 1..10000

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

William A. Stein, The modular forms database.

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

Formula

From Bruno Berselli, Jun 24 2010: (Start)

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

a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.

a(n) = (6*n + (-1)^n - 5)/2. (End)

a(n) = 6*n - a(n-1) - 8 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*A058764(k+1). - Philippe Deléham, Oct 17 2011

Sum_{n>=2} (-1)^n/a(n) = log(3)/4 - sqrt(3)*Pi/36. - Amiram Eldar, Dec 13 2021

E.g.f.: 2 + ((6*x -5)*exp(x) + exp(-x))/2. - David Lovler, Aug 25 2022

Mathematica

Flatten[{#, #+4}&/@(6Range[0, 30])] (* Harvey P. Dale, Jul 07 2013 *)

Prog

(PARI) forstep(n=0, 200, [4, 2], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Crossrefs

Cf. A047241: (6*n - (-1)^n - 5)/2.

Cf. A342819.

Sequence in context: A020189 A166986 A318487 * A194382 A296655 A310577

Adjacent sequences: A047230 A047231 A047232 * A047234 A047235 A047236

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved