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Search: id:A105613
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| A105613 |
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Self-convolution omits 1's at positions of triangular numbers less one. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Self-convolution is A105614.
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EXAMPLE
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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,...}.
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PROGRAM
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(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)))}
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CROSSREFS
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Cf. A105614.
Adjacent sequences: A105610 A105611 A105612 this_sequence A105614 A105615 A105616
Sequence in context: A008275 A130534 A107416 this_sequence A135894 A130850 A075263
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2005
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