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A180148 a(n) = 3*a(n-1)+a(n-2) with a(0)=2 and a(1)=5. 2
2, 5, 17, 56, 185, 611, 2018, 6665, 22013, 72704, 240125, 793079, 2619362, 8651165, 28572857, 94369736, 311682065, 1029415931, 3399929858, 11229205505, 37087546373, 122491844624, 404563080245, 1336181085359, 4413106336322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Inverse binomial transform of A052961 (without the leading 1).

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,1).

FORMULA

G.f.: (2-x)/(1-3*x-x^2).

a(n) = 3*a(n-1)+a(n-2) with a(0)=2 and a(1)=5.

a(n) = ((4+7*A)*A^(-n-1)+(4+7*B)*B^(-n-1))/13 with A=(-3+sqrt(13))/2 and B=(-3-sqrt(13))/2.

Limit(a(n+k)/a(k), k=infinity) = (-1)^n*2/(A006497(n)-A006190(n)*sqrt(13)).

PROG

(PARI) a(n)=([0, 1; 1, 3]^n*[2; 5])[1, 1] \\ Charles R Greathouse IV, Oct 13 2016

CROSSREFS

Cf. A003688, A052906.

Appears in A180142.

Sequence in context: A121193 A159866 A042671 * A241133 A148410 A190531

Adjacent sequences:  A180145 A180146 A180147 * A180149 A180150 A180151

KEYWORD

easy,nonn

AUTHOR

Johannes W. Meijer, Aug 13 2010

STATUS

approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)