A105613 - OEIS

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A105613

Self-convolution omits 1's at positions of triangular numbers less one.

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

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OFFSET

0,4

COMMENTS

Self-convolution is A105614.

LINKS

Table of n, a(n) for n=0..45.

EXAMPLE

Given this sequence:

A = [1, 1, 1, 2,3, 1, 6,11,12, 1, 24,48,71,78, 1, 155, ...],

the self-convolution yields:

A^2 = [1, 2,3, 6,11,12, 24,48,71,78, 155,272,420,652,903, ...],

giving this sequence with 1's omitted at positions {0,2,5,9,14,...}.

PROG

(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)))

CROSSREFS

Cf. A105614.

Sequence in context: A008275 A130534 A107416 * A334951 A263634 A135894

Adjacent sequences: A105610 A105611 A105612 * A105614 A105615 A105616

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 16 2005

STATUS

approved