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A163616 a(n) = ((1 + 3*sqrt(2))*(5 + sqrt(2))^n + (1 - 3*sqrt(2))*(5 - sqrt(2))^n)/2. 3
1, 11, 87, 617, 4169, 27499, 179103, 1158553, 7466161, 48014891, 308427207, 1979929577, 12705470009, 81516319819, 522937387983, 3354498523993, 21517425316321, 138020787111371, 885307088838327, 5678592784821737 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A163615. Fifth binomial transform of A163864. Inverse binomial transform of A081183 without initial 0.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-23).

FORMULA

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

G.f.: (1+x)/(1-10*x+23*x^2).

E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 30 2017

a(n) = A081182(n)+A081182(n+1). - R. J. Mathar, Jul 01 2022

MATHEMATICA

CoefficientList[Series[(1 + x)/(1 - 10 x + 23 x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jun 14 2014 *)

LinearRecurrence[{10, -23}, {1, 11}, 50] (* G. C. Greubel, Jul 30 2017 *)

PROG

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+r)^n+(1-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009

(PARI) x='x+O('x^50); Vec((1+x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Jul 30 2017

CROSSREFS

Cf. A163615, A163864, A081183.

Sequence in context: A232078 A016222 A081013 * A224182 A119383 A001278

Adjacent sequences:  A163613 A163614 A163615 * A163617 A163618 A163619

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009

STATUS

approved

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Last modified October 1 00:20 EDT 2022. Contains 357111 sequences. (Running on oeis4.)