Search: id:A072951
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%I A072951
%S A072951 1,2,4,6,11,15,27,39,63,100,159,247,403,641,1023,1644,2653,4264,6872,
%T A072951 11081,17895,28899,46680,75420,121918,197113,318728,515420,833592,
%U A072951 1348309,2181022,3528144,5707568,9233629,14938481,24168531,39102324
%N A072951 a(n)=sum(k>=2,z(k)*v(k)^n) where v(k) is the real positive solution to 
               x^k=x+1 (i.e. the k-th Pisot-Vijayaraghavan number) and z(k) is the 
               real positive root of a polynomial P(k,x) with integer coefficients 
               of degree k.
%C A072951 In particular a(n) is asymptotic to (1/10)*(5+sqrt(5))*phi^n where phi 
               is the golden ratio. First P(k,x) are P(2,x)=5x^2-5x-1; P(3,x)=23x^3-23x^2+8x-1; 
               P(4)=283x^4-283x^3+105x^2-17x+1; P(5)=2869x^5-2869x^4+1154x^3-234x^2+24x 
               -1
%F A072951 a(n)=sum(k=1, n, C(k, n modk)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 03 2003
%o A072951 (PARI) a(n)=sum(k=1,n,binomial(k,n%k))
%Y A072951 Sequence in context: A138461 A103580 A094866 this_sequence A062766 A115269 
               A103692
%Y A072951 Adjacent sequences: A072948 A072949 A072950 this_sequence A072952 A072953 
               A072954
%K A072951 easy,nonn
%O A072951 1,2
%A A072951 Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002

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