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Search: id:A136270
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| A136270 |
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a(n) = 20*a(n-1) - 3*a(n-2). |
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+0
1
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| 1, 17, 337, 6689, 132769, 2635313, 52307953, 1038253121, 20608138561, 409048011857, 8119135821457, 161155572393569, 3198754040407009, 63491614090959473, 1260236019697968433, 25014245551686490241
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OFFSET
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1,2
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COMMENT
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a(n)/a(n-1) tends to (sqrt(97) + 10), an eigenvalue of the matrix and root of the characteristic polynomial x^2 - 20x + 3.
A137246(n) = 20*a(n) - 3*a(n-1), n>4.
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FORMULA
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a(n) = 20*a(n-1) - 3*a(n-2), n>2; a(1) = 1, a(2) = 17. [a(3), a(4)] = the 2 X 2 matrix [0,1; -3,20]^n * [1,1].
O.g.f.: (1-3*x)/(1-20*x+3*x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Alexander R. Povolotsky (pevnev(AT)juno.com), Mar 31 2008
a(n) = (1/2)*(10 - sqrt(97))^n - (9/194)*sqrt(97)*(10 + sqrt(97))^n + (1/2)*(10 + sqrt(97))^n + (9/194)*(10 - sqrt(97))^n*sqrt(97) - Alexander R. Povolotsky (pevnev(AT)juno.com), Mar 31 2008
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EXAMPLE
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a(4) = 20*a(3) - 3*a(2) = 20*337 - 3*17.
[a(3), a(4)] = [0,1; -3,20] ^3 * [1,1] = [337, 6689].
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CROSSREFS
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Cf. A137246.
Adjacent sequences: A136267 A136268 A136269 this_sequence A136271 A136272 A136273
Sequence in context: A029535 A099275 A142933 this_sequence A009046 A012112 A137246
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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), Mar 19 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2008
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