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A163349
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
2
1, 9, 67, 463, 3089, 20241, 131363, 848087, 5459521, 35089209, 225323107, 1446179263, 9279361169, 59531488641, 381889579523, 2449671556487, 15713255235841, 100790106559209, 646496195167747, 4146789500815663
OFFSET
0,2
COMMENTS
Binomial transform of A081180 without initial 0. Fifth binomial transform of A143095.
FORMULA
a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
a(n) = ((1+2*sqrt(2))*(5+sqrt(2))^n + (1-2*sqrt(2))*(5-sqrt(2))^n)/2.
G.f.: (1-x)/(1-10*x+23*x^2).
E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016
MATHEMATICA
LinearRecurrence[{10, -23}, {1, 9}, 50] (* G. C. Greubel, Dec 19 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(5+r)^n+(1-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-x)/(1-10*x+23*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016
CROSSREFS
Sequence in context: A197277 A238317 A105287 * A016130 A115202 A287817
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009
STATUS
approved