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Search: id:A138229
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| A138229 |
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Expansion of (1-x)/(1-2x+6x^2). |
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+0
3
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| 1, 1, -4, -14, -4, 76, 176, -104, -1264, -1904, 3776, 18976, 15296, -83264, -258304, -17024, 1515776, 3133696, -2827264, -24456704, -31949824, 82840576, 357380096, 217716736, -1708847104, -4723994624, 805093376
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of [1, 0, -5, 0, 25, 0, -125, 0, 625, 0, ...]=: powers of -5 with interpolated zeros . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2008]
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FORMULA
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a(n)=2*a(n-1)-6*a(n-2), a(0)=1, a(1)=1 . a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-5)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n)=Sum_{k, 0<=k<=n}A124182(n,k)*(-6)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 15 2008]
a(n)=(1/2)*{[1-I*sqrt(5)]^n+[1+I*sqrt(5)]^n}, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 18 2008]
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PROGRAM
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sage: [lucas_number2(n, 2, 6)/2for n in xrange(0, 28)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Cf. A088139.
Sequence in context: A107775 A003117 A156985 this_sequence A131702 A029661 A133856
Adjacent sequences: A138226 A138227 A138228 this_sequence A138230 A138231 A138232
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 06 2008
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