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A056123 a(n) = 3a(n-1) - a(n-2); a(0)=1, a(1)=11. 0
1, 11, 32, 85, 223, 584, 1529, 4003, 10480, 27437, 71831, 188056, 492337, 1288955, 3374528, 8834629, 23129359, 60553448, 158530985, 415039507, 1086587536, 2844723101, 7447581767, 19498022200, 51046484833, 133641432299 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n)={11*[((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n]-[((3+sqrt(5))/2)^(n-1) - ((3-sqrt(5))/2)^(n-1)]}/sqrt(5).

G.f.: (1+8x)/(1-3x+x^2).

6*Lucas(2n+1) - Fibonacci(2n+5).

CROSSREFS

Cf. A055850.

Sequence in context: A007790 A195857 A048773 * A006655 A018956 A018947

Adjacent sequences:  A056120 A056121 A056122 * A056124 A056125 A056126

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jul 06 2000

STATUS

approved

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Last modified June 24 15:07 EDT 2017. Contains 288697 sequences.