A105614 Self-convolution of A105613.

1, 2, 3, 6, 11, 12, 24, 48, 71, 78, 155, 272, 420, 652, 903, 1364, 2144, 3436, 5955, 9668, 10838, 16408, 27948, 45920, 66817, 109296, 152786, 197542, 327755, 531440, 735565, 1083128, 1727206, 2521374, 3938246, 5248706, 8452114, 12093692

Offset

0,2

Links

Table of n, a(n) for n=0..37.

Example

Given sequence A105613:
[1, 1, 1, 2,3, 1, 6,11,12, 1, 24,48,71,78, ...],
the self-convolution yields this sequence:
[1, 2,3, 6,11,12, 24,48,71,78, ...],
which is A105613 with 1's omitted at positions {0,2,5,9,14,...}.

Prog

(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))}

Crossrefs

Cf. A105613.

Sequence in context: A284091 A004038 A152038 * A116441 A116051 A124593

Adjacent sequences: A105611 A105612 A105613 * A105615 A105616 A105617

Keyword

nonn

Author

Paul D. Hanna, Apr 16 2005

Status

approved