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A110422
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a(n)=sum((-1)^(r+1)*(n-r)*r,r=1..floor(n/2)).
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0
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1, 2, -1, -2, 6, 8, -6, -8, 15, 18, -15, -18, 28, 32, -28, -32, 45, 50, -45, -50, 66, 72, -66, -72, 91, 98, -91, -98, 120, 128, -120, -128, 153, 162, -153, -162, 190, 200, -190, -200, 231, 242, -231, -242, 276, 288, -276, -288, 325, 338, -325, -338, 378, 392, -378, -392, 435, 450, -435, -450, 496, 512, -496, -512, 561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| a(4n)=-a(4n-2); a(4n+1)=-a(4n-1). If sum in definition is not alternating one obtains A023855. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2005
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FORMULA
| a(2n)=(1/2)n-(-1)^n*(1/2)n^2; a(2n-1)=(1/2)n-(1/4)+(-1)^n*(1/4)(2n^2-2n+1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2005
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EXAMPLE
| a(8)=-6 because 7*1-6*2+5*3-4*4=-6.
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MAPLE
| a:=n->sum((-1)^(r+1)*(n-r)*r, r=1..floor(n/2)): seq(a(n), n=2..70); (Deutsch)
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CROSSREFS
| Cf. A023855.
Sequence in context: A059587 A070236 A020825 * A131804 A170829 A032085
Adjacent sequences: A110419 A110420 A110421 * A110423 A110424 A110425
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KEYWORD
| easy,sign
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 01 2005
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EXTENSIONS
| Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2005
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