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Search: id:A140165
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| A140165 |
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a(n) = (-1)* a(n-1) + 3*a(n-2). |
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+0
3
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| 1, 2, 1, 5, -2, 17, -23, 74, -143, 365, -794, 1889, -4271, 9938, -22751, 52565, -120818, 278513, -640967, 1476506, -3399407, 7828925, -18027146, 41513921, -95595359, 220137122, -506923199, 1167334565
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = row sums of triangle A140166.
A140167 is a companion sequence.
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FORMULA
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a(n) = (-1)*a(n-1) + 3*a(n-2), given a(1) = 1, a(2) = 2. a(n) = term (1,1) of X^n, where X = the 2x2 matrix [1,-1; -1,-2].
a(n)=(1/2)*[-1/2+(1/2)*sqrt(13)]^n+(1/2)*[-1/2-(1/2)*sqrt(13)]^n-(5/26)*sqrt(13)*[-1/2-(1/2) *sqrt(13)]^n+(5/26)*[-1/2+(1/2)*sqrt(13)]^n*sqrt(13), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 01 2008]
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EXAMPLE
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a(6) = 17 = (-1)*a(5) + 3*a(4) = (-1)*(-2) + 3*5.
a(4) = 5 = term (1,1) of X^5, where X^5 = [5,7; 7,26].
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CROSSREFS
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Cf. A140166, A140167.
Adjacent sequences: A140162 A140163 A140164 this_sequence A140166 A140167 A140168
Sequence in context: A143891 A030400 A115345 this_sequence A141483 A104731 A105728
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KEYWORD
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sign
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2008
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