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Self-convolution of A105613.
1

%I #3 Mar 30 2012 18:36:45

%S 1,2,3,6,11,12,24,48,71,78,155,272,420,652,903,1364,2144,3436,5955,

%T 9668,10838,16408,27948,45920,66817,109296,152786,197542,327755,

%U 531440,735565,1083128,1727206,2521374,3938246,5248706,8452114,12093692

%N Self-convolution of A105613.

%e Given sequence A105613:

%e [1, 1, 1, 2,3, 1, 6,11,12, 1, 24,48,71,78, ...],

%e the self-convolution yields this sequence:

%e [1, 2,3, 6,11,12, 24,48,71,78, ...],

%e which is A105613 with 1's omitted at positions {0,2,5,9,14,...}.

%o (PARI) {a(n)=local(V,t);if(n==0,1,V=vector(n+1,k, t=ceil((sqrt(8*k+1)-1)/2);if(ceil((sqrt(8*k+9)-1)/2)-t==1,1,a(k-t))); polcoeff(Ser(V)^2+x*O(x^n),n))}

%Y Cf. A105613.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 16 2005