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A047233 Numbers that are congruent to {0, 4} mod 6. 8
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 (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
William A. Stein, The modular forms database.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)