Search: id:A105613
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%I A105613
%S A105613 1,1,1,2,3,1,6,11,12,1,24,48,71,78,1,155,272,420,652,903,1,1364,2144,
%T A105613 3436,5955,9668,10838,1,16408,27948,45920,66817,109296,152786,197542,1,
%U A105613 327755,531440,735565,1083128,1727206,2521374,3938246,5248706,1,8452114
%N A105613 Self-convolution omits 1's at positions of triangular numbers less one.
%C A105613 Self-convolution is A105614.
%e A105613 Given this sequence:
%e A105613 A = [1, 1, 1, 2,3, 1, 6,11,12, 1, 24,48,71,78, 1, 155, ...],
%e A105613 the self-convolution yields:
%e A105613 A^2 = [1, 2,3, 6,11,12, 24,48,71,78, 155,272,420,652,903, ...],
%e A105613 giving this sequence with 1's omitted at positions {0,2,5,9,14,...}.
%o A105613 (PARI) {a(n)=local(V,t);if(n==0|n==1,1,t=ceil((sqrt(8*n+9)-1)/2); if(ceil((sqrt(8*n+17)-1)/
               2)-t==1,1,V=vector(n-t+2,k,a(k-1)); polcoeff(Ser(V)^2+O(x^(n-t+2)),
               n-t+1)))}
%Y A105613 Cf. A105614.
%Y A105613 Sequence in context: A008275 A130534 A107416 this_sequence A135894 A130850 
               A075263
%Y A105613 Adjacent sequences: A105610 A105611 A105612 this_sequence A105614 A105615 
               A105616
%K A105613 nonn
%O A105613 0,4
%A A105613 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2005

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