Search: id:A035959
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%I A035959
%S A035959 1,1,2,3,5,6,10,13,19,25,34,44,60,76,100,127,164,205,262,325,409,505,
%T A035959 628,769,950,1156,1414,1713,2081,2505,3026,3625,4352,5192,6200,7364,
%U A035959 8756,10357,12258,14450,17034,20006,23500,27510,32200,37582,43846,51022
%N A035959 Number of partitions of n in which no parts are multiples of 5.
%C A035959 Also number of partitions with at most 4 parts of size 1 and differences 
               between parts at distance 6 are greater than 1.
%C A035959 Also number of partitions of n where no part appears more than four times.
%C A035959 Case k=7,i=5 of Gordon Theorem.
%D A035959 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%D A035959 Watson, G. N.; Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine 
               Angew. Math. (Crelle), 179 (1938), 97-128. See the expression Y = 
               B/C in the notation of p. 106. [Added by njas, Nov 13 2009]
%H A035959 T. D. Noe, <a href="b035959.txt">Table of n, a(n) for n=0..1000</a>
%H A035959 GDZ, <a href="http://gdz.sub.uni-goettingen.de/no_cache/dms/load/toc/
               ?IDDOC=238618">Digitized volumes of Crelle</a> [Added by njas, Nov 
               13 2009]
%H A035959 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PartitionFunctionb.html">Link to a section of The World of Mathematics.</
               a>
%F A035959 G.f.: Prod_{j=1, oo} (1 + x^j + x^2j + x^3j + x^4j) - Jon Perry (perry(AT)globalnet.co.uk), 
               Mar 30 2004
%F A035959 G.f.: Prod_{n>0, n==1, 2, 3, 4 mod 5} 1/(1-q^n).
%F A035959 Given g.f. A(x) then B(x)=x*A(x^3)^2 satisfies 0=f(B(x), B(x^2)) where 
               f(u,v)= u^3 +v^3 -u*v -5*u^2*v^2 . - Michael Somos May 28 2006
%F A035959 Given g.f. A(x) then B(x)=x*A(x^3)^2 satisfies 0=f(B(x), B(x^2), B(x^4)) 
               where f(u,v,w)= +v +5*v^2*(u+w) -(u^2+u*w+w^2) . - Michael Somos 
               May 28 2006
%F A035959 Euler transform of period 5 sequence [ 1, 1, 1, 1, 0, ...]. - Michael 
               Somos May 28 2006
%F A035959 G.f. is product k>0 P5(x^k) where P5 is 5th cyclotomic polynomial.
%o A035959 (PARI) {a(n)=if(n<0, 0, polcoeff( eta(x^5+x*O(x^n))/ eta(x+x*O(x^n)), 
               n))} /* Michael Somos May 28 2006 */
%Y A035959 Cf. A000726, A001935, A000009, A061198, A061199.
%Y A035959 Sequence in context: A018429 A035953 A087750 this_sequence A036801 A035966 
               A035974
%Y A035959 Adjacent sequences: A035956 A035957 A035958 this_sequence A035960 A035961 
               A035962
%K A035959 nonn,easy,nice,new
%O A035959 0,3
%A A035959 Olivier Gerard (olivier.gerard(AT)gmail.com)

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