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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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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; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 1..54000.
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FORMULA
| 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
| 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
| 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
| Cf. A000217, A136108.
Sequence in context: A091090 A066075 A072347 * A178691 A124768 A072527
Adjacent sequences: A136104 A136105 A136106 * A136108 A136109 A136110
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 12 2007
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