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A206776 a(n) = 3*a(n-1) + 2*a(n-2) 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 (list; graph; refs; listen; history; text; internal format)
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 entries for linear recurrences with constant coefficients, signature (3,2).

FORMULA

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

a(n) = ((3-sqrt(17))^n+(3+sqrt(17))^n)/2^n.

a(n) = [x^n] ( (1 + 3*x + sqrt(1 + 6*x + 17*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015

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(n-1): n in [0..25]];

(Maxima) a[0]:2$ a[1]:3$ a[n]:=3*a[n-1]+2*a[n-2]$ makelist(a[n], n, 0, 25);

(PARI) Vec((2-3*x)/(1-3*x-2*x^2) + O(x^30)) \\ Michel Marcus, Jun 26 2015

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

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Last modified August 28 13:24 EDT 2015. Contains 261122 sequences.