

A180148


a(n) = 3*a(n1)+a(n2) 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.: (2x)/(13*xx^2).
a(n) = 3*a(n1)+a(n2) with a(0)=2 and a(1)=5.
a(n) = ((4+7*A)*A^(n1)+(4+7*B)*B^(n1))/13 with A=(3+sqrt(13))/2 and B=(3sqrt(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



