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Search: id:A100050
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| A100050 |
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A Chebyshev transform of n. |
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+0
2
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| 0, 1, 2, 0, -4, -5, 0, 7, 8, 0, -10, -11, 0, 13, 14, 0, -16, -17, 0, 19, 20, 0, -22, -23, 0, 25, 26, 0, -28, -29, 0, 31, 32, 0, -34, -35, 0, 37, 38, 0, -40, -41, 0, 43, 44, 0, -46, -47, 0, 49, 50, 0, -52, -53, 0, 55, 56, 0, -58, -59, 0, 61, 62, 0, -64, -65, 0, 67, 68, 0, -70, -71, 0, 73, 74, 0, -76, -77, 0, 79, 80, 0, -82, -83, 0, 85, 86, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A Chebyshev transform of x/(1-x)^2: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
Fully multiplicative with a(p) = 0 if p = 3; p otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 10, 2005.
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FORMULA
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G.f.: x(1-x^2)/(1-x+x^2)^2; a(n)=2a(n-1)-3a(n-2)+2a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)*(n-2k)/(n-k)}.
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PROGRAM
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sage: [lucas_number1(n, 2, 1)*lucas_number1(n, 1, 1) for n in xrange(0, 88)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 06 2008
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CROSSREFS
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Cf. A099837, A099443, A011655, A100047, A100048, A100051, A091684.
Sequence in context: A070692 A091684 A162397 this_sequence A164616 A004482 A111677
Adjacent sequences: A100047 A100048 A100049 this_sequence A100051 A100052 A100053
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KEYWORD
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easy,sign,mult
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 31 2004
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