Search: id:A008586
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%I A008586
%S A008586 0,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,
%T A008586 76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,
%U A008586 136,140,144,148,152,156,160,164,168,172,176,180,184
%N A008586 Multiples of 4.
%C A008586 Apart from initial term(s), dimension of the space of weight 2n cusp 
               forms for Gamma_0( 14 ).
%C A008586 A000466(n), A008586(n) and A053755(n) are Pythagorean triples. - Zak 
               Seidov, Jan 16 2007
%C A008586 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
%C A008586 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]
%D A008586 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 3.
%H A008586 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A008586 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A008586 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=316">
               Encyclopedia of Combinatorial Structures 316</a>
%H A008586 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/dimskg0n.gp">
               Dimensions of the spaces S_k(Gamma_0(N))</a>
%H A008586 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/">The 
               modular forms database</a>
%H A008586 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DoublyEvenNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A008586 a(n)=C(n+0,1)*4^1, n>=0 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Aug 06 2008]
%F A008586 a(n)=A008574(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 28 2008]
%F A008586 a(n)=8*n-a(n-1)-12 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 24 2009]
%e A008586 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]
%p A008586 with(finance):seq(add(cashflows([0,0,4], 0 ),k=1..n),n=0..58); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008
%p A008586 seq(binomial(n+0,1)*4^1, n=0..44); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Aug 06 2008]
%t A008586 lst={};Do[AppendTo[lst, 4*n], {n, 6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Aug 29 2008]
%o A008586 (Other) sage: [i for i in range(186) if gcd(4,i) == 4] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2009]
%o A008586 (Other) sage: [n-crt(2, n, 3, 4) for n in xrange(2, 49)] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2009]
%Y A008586 A038231, A035008 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Aug 06 2008]
%Y A008586 Sequence in context: A100716 A076310 A161352 this_sequence A059558 A008574 
               A085127
%Y A008586 Adjacent sequences: A008583 A008584 A008585 this_sequence A008587 A008588 
               A008589
%K A008586 nonn,new
%O A008586 0,2
%A A008586 N. J. A. Sloane (njas(AT)research.att.com).

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