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Search: id:A062781
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| A062781 |
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Number of arithmetic progressions of four terms and any mean which can be extracted from the set of the first n positive integers. |
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+0
2
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| 0, 0, 0, 1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51, 57, 63, 70, 77, 84, 92, 100, 108, 117, 126, 135, 145, 155, 165, 176, 187, 198, 210, 222, 234, 247, 260, 273, 287, 301, 315, 330, 345, 360, 376, 392
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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This sequence seems to be a shifted version of the Somos sequence A058937.
Equal to the partial sums of A002264 (cf. A130518) but with initial index 1 instead of 0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
Apart from offset, the same as A130518. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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LINKS
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M. Somos, Somos Polynomials
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FORMULA
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a(n)=P(n, 4), where: P[n, k] = n*Floor[n/(k - 1)] - (1/2)(k - 1)(Floor[n/(k - 1)]*(Floor[n/(k - 1)] + 1)) recursion: a(n)=a(n-3)+n-3; a(1)=a(2)=a(3)=0
a(n)=1/2*floor((n-1)/3)*(2n-3-3*floor((n-1)/3)). G.f.: g(x)=x^4/((1-x^3)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
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PROGRAM
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(Other) sage: [floor(binomial(n, 2)/3) for n in xrange(0, 50)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
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CROSSREFS
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Cf. A058937, A001840.
Cf. A002620, A130519, A130520.
Sequence in context: A120431 A024195 A071423 this_sequence A145919 A058937 A130518
Adjacent sequences: A062778 A062779 A062780 this_sequence A062782 A062783 A062784
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KEYWORD
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nonn,new
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AUTHOR
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Santi Spadaro (spados(AT)katamail.com), Jul 18 2001
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