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Search: id:A137501
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| A137501 |
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The even numbers repeated and with the sign changed. |
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+0
2
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| 0, 0, 2, -2, 4, -4, 6, -6, 8, -8, 10, -10, 12, -12, 14, -14, 16, -16, 18, -18, 20, -20, 22, -22, 24, -24, 26, -26, 28, -28, 30, -30, 32, -32, 34, -34, 36, -36, 38, -38, 40, -40, 42, -42, 44, -44, 46, -46, 48, -48, 50, -50, 52, -52, 54, -54, 56, -56, 58, -58, 60, -60, 62, -62, 64, -64, 66, -66, 68, -68, 70, -70, 72, -72, 74
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Peter Luschny (peter(AT)luschny.de), Jul 12 2009: (Start)
The general formula for alternating sums of powers of even integers is in terms of the Swiss-Knife polynomials P(n,x) A153641 (P(n,1)-(-1)^k P(n,2k+1))/2. Here n=1 and k shifted one place, thus
a(k) = (P(1,1)-(-1)^(k-1) P(1,2(k-1)+1))/2. (End)
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FORMULA
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a(n) = ( n - (1/2) + (1/2)*(-1)^n )*(-1)^n
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MAPLE
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den:= n -> (n-1/2+1/2*(-1)^n)*(-1)^n: seq(den(n), n=-10..10);
a := n -> (1+(-1)^n*(2*n-1))/2; [From Peter Luschny (peter(AT)luschny.de), Jul 12 2009]
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CROSSREFS
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Cf. A052928.
Sequence in context: A161764 A131055 A052928 this_sequence A005186 A008642 A001364
Adjacent sequences: A137498 A137499 A137500 this_sequence A137502 A137503 A137504
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KEYWORD
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easy,sign
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AUTHOR
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Carlos Alberto da Costa Filho (cacau_dacosta(AT)hotmail.com), Apr 22 2008
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