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Search: id:A008586
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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]
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 3.
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LINKS
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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, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=C(n+0,1)*4^1, n>=0 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
a(n)=A008574(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2008]
a(n)=8*n-a(n-1)-12 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]
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EXAMPLE
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For n=2, a(2)=8*2-0-12=4; n=3, a(3)=8*3-4-12=8; n=4, a(4)=8*4-8-12=12 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]
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MAPLE
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with(finance):seq(add(cashflows([0, 0, 4], 0 ), k=1..n), n=0..58); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008
seq(binomial(n+0, 1)*4^1, n=0..44); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, 4*n], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 29 2008]
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PROGRAM
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(Other) sage: [i for i in range(186) if gcd(4, i) == 4] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2009]
(Other) sage: [n-crt(2, n, 3, 4) for n in xrange(2, 49)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2009]
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CROSSREFS
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A038231, A035008 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
Sequence in context: A100716 A076310 A161352 this_sequence A059558 A008574 A085127
Adjacent sequences: A008583 A008584 A008585 this_sequence A008587 A008588 A008589
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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