

A206776


a(n) = 3*a(n1) + 2*a(n2) for n>1, a(0)=2, a(1)=3.


2



2, 3, 13, 45, 161, 573, 2041, 7269, 25889, 92205, 328393, 1169589, 4165553, 14835837, 52838617, 188187525, 670239809, 2387094477, 8501763049, 30279478101, 107841960401, 384084837405, 1367938433017, 4871984973861, 17351831787617, 61799465310573
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OFFSET

0,1


COMMENTS

This is the Lucas sequence V(3,2).
Inverse binomial transform of this sequence is A072265.
Is a(n)+1 = A124805(n) for n>0?


LINKS

Bruno Berselli, Table of n, a(n) for n = 0..200
Wikipedia, Lucas sequence: Specific names.
Index to sequences with linear recurrences with constant coefficients, signature (3,2).


FORMULA

G.f.: (23*x)/(13*x2*x^2).
a(n) = ((3sqrt(17))^n+(3+sqrt(17))^n)/2^n.


MATHEMATICA

RecurrenceTable[{a[n] == 3 a[n  1] + 2 a[n  2], a[0] == 2, a[1] == 3}, a[n], {n, 25}]
LinearRecurrence[{3, 2}, {2, 3}, 30] (* Harvey P. Dale, Apr 29 2014 *)


PROG

(MAGMA) [n le 1 select n+2 else 3*Self(n)+2*Self(n1): n in [0..25]];
(Maxima) a[0]:2$ a[1]:3$ a[n]:=3*a[n1]+2*a[n2]$ makelist(a[n], n, 0, 25);


CROSSREFS

Cf. A189736 (same recurrence but with initial values reversed).
Sequence in context: A235626 A164133 A226938 * A214888 A203985 A164511
Adjacent sequences: A206773 A206774 A206775 * A206777 A206778 A206779


KEYWORD

nonn,easy


AUTHOR

Bruno Berselli, Jan 10 2013


STATUS

approved



