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A047233 Numbers that are congruent to {0, 4} mod 6. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)