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A163348 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7. 1
1, 7, 35, 161, 721, 3199, 14147, 62489, 275905, 1218007, 5376707, 23734193, 104768209, 462469903, 2041441955, 9011362409, 39778080769, 175588947751, 775087121123, 3421400092481, 15102790707025, 66666943594783 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A111566. Third binomial transform of A143095. Inverse binomial transform of A081180 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 (6,-7).

FORMULA

a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

a(n) = ((1+2*sqrt(2))*(3+sqrt(2))^n + (1-2*sqrt(2))*(3-sqrt(2))^n)/2.

G.f.: (1+x)/(1-6*x+7*x^2).

E.g.f.: exp(3*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016

a(n) = A081179(n)+A081179(n+1). - R. J. Mathar, Feb 04 2021

MATHEMATICA

LinearRecurrence[{6, -7}, {1, 7}, 50] (* G. C. Greubel, Dec 19 2016 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(3+r)^n+(1-2*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009

(PARI) Vec((1+x)/(1-6*x+7*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016

CROSSREFS

Cf. A111566, A143095 (1,4,2,8,4,16,...), A081180.

Sequence in context: A005003 A243382 A242577 * A291237 A037099 A055421

Adjacent sequences:  A163345 A163346 A163347 * A163349 A163350 A163351

KEYWORD

nonn,easy

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

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)