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Search: id:A136107
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| A136107 |
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Number of representations of n as the difference of two positive triangular numbers. |
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+0
6
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| 0, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 4, 1, 2, 4, 2, 1, 4, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 5, 2, 2, 2, 3, 3, 4, 2, 2, 4, 3, 2, 4, 2, 2, 4, 2, 2, 6, 1, 4, 3, 2, 2, 4, 4, 2, 3, 2, 2, 6, 2, 4, 3, 2, 2, 5, 2, 2, 4, 4, 2, 4, 2, 2, 6, 3, 2, 4, 2, 4, 2, 2, 3, 6, 3, 2, 4, 2, 2, 7
(list; graph; listen)
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OFFSET
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1,5
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..54000.
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FORMULA
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G.f.: Sum(x^((n^2+3*n)/2)/(1-x^n),n=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 13 2008
a(n) = A001227(n) - A010054(n) [From Max Alekseyev (maxale(AT)gmail.com), May 13 2009]
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EXAMPLE
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a(2)=1 because 3-1 = 2,
a(5)=2 because 6-1 = 15-10 = 5,
a(9)=3 because 10-1 = 15-6 = 45-36 = 9, etc.
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MATHEMATICA
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f[n_] := Block[{c = 0, k = 1}, While[k < n, If[ IntegerQ[ Sqrt[8 n + 4 k (k + 1) + 1]], c++ ]; k++ ]; c]; Table[f@n, {n, 105}]
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CROSSREFS
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Cf. A000217, A136108.
Sequence in context: A091090 A066075 A072347 this_sequence A124768 A072527 A081373
Adjacent sequences: A136104 A136105 A136106 this_sequence A136108 A136109 A136110
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 12 2007
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