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Search: id:A120612
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| A120612 |
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For n>2, a(n) = 2*a(n-1) + 15*a(n-2). |
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+0
4
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| 1, 17, 49, 353, 1441, 8177, 37969, 198593, 966721, 4912337, 24325489, 122336033, 609554401, 3054149297, 15251614609, 76315468673, 381405156481, 1907542343057, 9536162033329, 47685459212513, 238413348924961
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Characteristic polynomial of matrix M = x^2 - 2x - 15. a(n)/a(n-1) tends to 5, largest eigenvalue of M, and a root of the characteristic polynomial.
a(2n+1) = A005059(2n+1) = {1,49,1441,37969,966721,...} = (5^(2n+1) - 3^(2n+1))/2. a(2n) = A081186(2n) = {17,353,8177,198593,...} = (3^(2n) + 5^(2n))/2, 4th binomial transform of (1,0,1,0,1,......), A059841. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 31 2006
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FORMULA
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Let M = the 2 X 2 matrix [1,4; 4,1], then a(n) = M^n * [1,0], left term.
a(n) = ( 5^n + (-1)^n * 3^n ) / 2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 31 2006
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*16^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007
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EXAMPLE
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a(4) = 353 = 2*49 + 15* 17 = 2*a(3) + 15*a(2).
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MATHEMATICA
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Table[(5^n+(-1)^n*3^n)/2, {n, 1, 30}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 31 2006
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CROSSREFS
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Cf. A005059, A081186, A059841.
Adjacent sequences: A120609 A120610 A120611 this_sequence A120613 A120614 A120615
Sequence in context: A113867 A049737 A126371 this_sequence A098329 A003124 A005570
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 17 2006
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EXTENSIONS
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More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 31 2006
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