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Search: id:A130206
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| A130206 |
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a(1) = 1, a(2) = 2; for n>2, a(n) = t(n)-a(n-1)-a(n-2), where t(n) = n(n+1)/2 = triangular number A000217. |
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3
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| 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, 408, 425, 442, 459, 477, 495, 513, 532, 551, 570, 590
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Any three consecutive terms sum up to a triangular number. Essentially A001840.
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FORMULA
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G.f.: x/(1+x+x^2)/(1-x)^3 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
a(n) = (4+3*n^2+9*n)/18+((n mod 3)-((n-1) mod 3))/9. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 01 2009]
a(n) = a(n-1)+a(n-3)-a(n-4)+1 for n > 4; a(1)=1, a(2)=2, a(3)=3, a(4)=5. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 04 2009]
a(n) = a(n-1)+a(n-3)-a(n-4)+1 for n > 4; a(1)=1, a(2)=2, a(3)=3, a(4)=5. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 15 2009]
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EXAMPLE
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1+2+3=6=t(3), 2+3+5=t(4), 5+7+9=t(5).
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MATHEMATICA
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a[1]=1; a[2]=2; a[n_]:=a[n]=n(n+1)/2-a[n-1]-a[n-2]; Table[a[n], {n, 100}]
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PROGRAM
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(MAGMA) [ n le 2 select n else n*(n+1)/2-Self(n-1)-Self(n-2): n in [1..58] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 01 2009]
(Other) sage: [floor(binomial(n, 2)/3) for n in xrange(3, 61)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
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CROSSREFS
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Cf. A000217, A001840, A130205.
Sequence in context: A058937 A130518 A001840 this_sequence A022794 A025693 A117930
Adjacent sequences: A130203 A130204 A130205 this_sequence A130207 A130208 A130209
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KEYWORD
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nonn,new
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), May 16 2007
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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