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A008586
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Multiples of 4.
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66
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0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 14 ).
A000466(n), A008586(n) and A053755(n) are Pythagorean triples. - Zak Seidov, Jan 16 2007
If X is an n-set and Y and Z disjoint 2-subsets of X then a(n-3) is equal to the number of 3-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Aug 26 2007
Number of n permutations (n>=1) of 5 objects u, v, z, x, y with repetition allowed, containing n-1 u's. Example: if n=1 then n-1 =zero (0) u, a(1)=4 because we have v, z, x, y. If n=2 then n-1= one (1) u, a(2)=8 because we have vu, zu, xu, yu, uv, uz, ux, uy. A038231 formatted as a triangular array:diagonal :4,8,12,16,20,24,28,32... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
For n > 0: numbers having more even than odd divisors: A048272(a(n)) < 0. [Reinhard Zumkeller, Jan 21 2012]
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 3.
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LINKS
| Milan Janjic, Two Enumerative Functions
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 316
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Eric Weisstein's World of Mathematics, Doubly Even Number
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
| a(n)=A008574(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2008]
a(n)=Sum_k>=0 {A030308(n,k)*2^(k+2)}. - From DELEHAM Philippe, Oct 17 2011.
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MATHEMATICA
| Range[0, 500, 4] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 26 2011 *)
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PROG
| (PARI) a(n)=n<<2 \\ Charles R Greathouse IV, Oct 17 2011
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CROSSREFS
| Cf. A038231, A035008.
Sequence in context: A191677 A076310 A161352 * A059558 A008574 A189917
Adjacent sequences: A008583 A008584 A008585 * A008587 A008588 A008589
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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