Search: id:A008616
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%I A008616
%S A008616 1,0,1,0,1,1,1,1,1,1,2,1,2,1,2,2,2,2,2,2,3,2,3,2,3,3,3,3,3,3,4,3,4,3,4,
%T A008616 4,4,4,4,4,5,4,5,4,5,5,5,5,5,5,6,5,6,5,6,6,6,6,6,6,7,6,7,6,7,7,7,7,7,7,
%U A008616 8,7,8,7,8,8,8,8,8,8,9,8,9,8,9,9,9,9,9,9,10,9,10,9,10,10,10,10,10,10
%N A008616 Expansion of 1/((1-x^2)(1-x^5)).
%C A008616 Number of partitions of n into parts of size two and five.
%C A008616 It appears that, for n>=2, a(n-2) is also (1) the number of partitions 
               of 3n that are 6-term arithmetic progressions and (2) Floor[n/2]-Floor[2n/
               5]. [From John W. Layman (layman(AT)math.vt.edu), Jun 29 2009]
%D A008616 D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, 
               p. 100.
%D A008616 G. E. Andrews, K. Eriksson, Integer Partitions, Cambridge Univ. Press, 
               2004. page 30 Exer. 48
%H A008616 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A008616 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=213">
               Encyclopedia of Combinatorial Structures 213</a>
%F A008616 G.f.: 1/((1-x^2)(1-x^5)).
%F A008616 Euler transform of finite sequence [0, 1, 0, 0, 1].
%F A008616 a(n) = -a(-7-n) = a(n-10)+1 = a(n-2)+a(n-5)-a(n-7). - Michael Somos Jan 
               25 2005
%F A008616 a(n)=7/20+n/10+(-1)^n/4+(A105384(n)+2*( A010891(n)+A105384(n+4)))/5. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 28 2009]
%o A008616 (PARI) a(n)=polcoeff(1/((1-x^2)*(1-x^5))+x*O(x^n),n)
%o A008616 (PARI) {a(n)=if(n<-6, -a(-7-n), polcoeff( 1/(1-x^2)/(1-x^5)+x*O(x^n), 
               n))} /* Michael Somos Jan 25 2005 */
%Y A008616 A000217(a(n))=A0025810(n).
%Y A008616 A008615 [From John W. Layman (layman(AT)math.vt.edu), Jun 29 2009]
%Y A008616 Sequence in context: A083023 A084359 A143935 this_sequence A097471 A025868 
               A050252
%Y A008616 Adjacent sequences: A008613 A008614 A008615 this_sequence A008617 A008618 
               A008619
%K A008616 nonn,easy
%O A008616 0,11
%A A008616 N. J. A. Sloane (njas(AT)research.att.com).

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