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A130518
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Sum {0<=k<=n, floor(k/3)} (Partial sums of A002264).
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3
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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, 408, 425, 442, 459, 477, 495, 513, 532, 551, 570
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Complementary with A130481 regarding triangular numbers, in that A130481(n)+3*a(n)=n(n+1)/2=A000217(n).
Apart from offset, the same as A062781. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
Apart from offset, the same as A001840. - Michael Somos, Sep 18 2010
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| G.f.: g(x)=x^3/((1-x^3)*(1-x)^2).
a(n) = +2*a(n-1) -1*a(n-2) +1*a(n-3) -2*a(n-4) +1*a(n-5).
a(n)=1/2*floor(n/3)*(2n-1-3*floor(n/3))))=A002264(n)*(2n-1-3*A002264(n))/2.
a(n)=1/2*A002264(n)*(n-1+A010872(n)).
a(n) = round(n*(n-1)/6) = round((n^2-n-1)/6) = floor(n*(n-1)/6) = ceil((n+1)*(n-2)/6). [From Mircea Merca (mircea(AT)teacher.com), Nov 28 2010]
a(n) = a(n-3)+n-2, n>2. [From Mircea Merca (mircea(AT)teacher.com), Nov 28 2010]
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PROG
| (Sage) [floor(binomial(n, 2)/3) for n in xrange(0, 60)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
(MAGMA) [Round(n*(n-1)/6): n in [0..60]]; // Vincenzo Librandi, Jun 25 2011
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CROSSREFS
| Cf. A002265, A002266, A004526, A010872, A010873, A010874, A062781, A130482, A130483.
Sequence in context: A062781 A145919 A058937 * A001840 A022794 A025693
Adjacent sequences: A130515 A130516 A130517 * A130519 A130520 A130521
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
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