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A083392
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Alternating partial sums of A000217.
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2
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0, -1, 2, -4, 6, -9, 12, -16, 20, -25, 30, -36, 42, -49, 56, -64, 72, -81, 90, -100, 110, -121, 132, -144, 156, -169, 182, -196, 210, -225, 240, -256, 272, -289, 306, -324, 342, -361, 380, -400, 420, -441, 462, -484, 506, -529, 552, -576, 600, -625, 650, -676, 702
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| William A. Tedeschi, Table of n, a(n) for n=0..10000
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FORMULA
| Sum{i=0, n, (-1)^i*t(i)} where t(i)=i*(i+1)/2
a(n)= -2*a(n-1) +2*a(n-3) +a(n-4). G.f.: x/((x-1)*(1+x)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 09 2010]
a(n) = (-1)^n * [(n^2+n)/2 - floor(n^2/4)] [From William A. Tedeschi (fynmun(AT)att.net), Aug 24 2010]
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EXAMPLE
| a(4)=t(0)-t(1)+t(2)-t(3)+t(4)=0-1+3-6+10=6
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PROG
| (PARI) t(n)=n*(n+1)/2 for (n=0, 30, print1(sum(i=0, n, (-1)^i*t(i))", "))
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CROSSREFS
| Cf. A000217, A002620.
Sequence in context: A194254 A086378 A088900 * A076921 A002620 A087811
Adjacent sequences: A083389 A083390 A083391 * A083393 A083394 A083395
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KEYWORD
| sign
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jun 11 2003
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EXTENSIONS
| More terms from David W. Wilson, Jun 14 2003
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