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A136270
a(n) = 20*a(n-1) - 3*a(n-2).
1
1, 17, 337, 6689, 132769, 2635313, 52307953, 1038253121, 20608138561, 409048011857, 8119135821457, 161155572393569, 3198754040407009, 63491614090959473, 1260236019697968433, 25014245551686490241
OFFSET
1,2
COMMENTS
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.
FORMULA
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].
A137246(n) = 20*a(n) - 3*a(n-1), n>4.
O.g.f.: (1-3*x)/(1-20*x+3*x^2). - R. J. Mathar and Alexander R. Povolotsky, 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, Mar 31 2008
EXAMPLE
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].
MATHEMATICA
LinearRecurrence[{20, -3}, {1, 17}, 50] (* G. C. Greubel, Feb 23 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-3*x)/(1-20*x+3*x^2)) \\ G. C. Greubel, Feb 23 2017
CROSSREFS
Cf. A137246.
Sequence in context: A318597 A142933 A180676 * A009046 A012112 A294435
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Mar 19 2008
STATUS
approved