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A022113 Fibonacci sequence beginning 2, 7. 7
2, 7, 9, 16, 25, 41, 66, 107, 173, 280, 453, 733, 1186, 1919, 3105, 5024, 8129, 13153, 21282, 34435, 55717, 90152, 145869, 236021, 381890, 617911, 999801, 1617712, 2617513, 4235225, 6852738, 11087963, 17940701, 29028664, 46969365, 75998029, 122967394 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

H. S. M. Coxeter, Introduction to Geometry, Second Edition, Wiley Classics Library Edition Published 1989, p. 172.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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

FORMULA

From Colin Barker, Oct 18 2013: (Start)

G.f.: -(5*x + 2)/(x^2 + x - 1).

a(n) = a(n-1) + a(n-2). (End)

a(n) = ((5+6*sqrt(5))/5)*((1+sqrt(5))/2)^n + ((5-6*sqrt(5))/5)*((1-sqrt(5))/2)^n starting at n=0. - Bogart B. Strauss, Oct 27 2013

a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=5, k=1. - Bruno Berselli, Feb 20 2017

MATHEMATICA

RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == a[n - 1] + a[n - 2]}, a, {n, 0, 40}] (* Bruno Berselli, Mar 12 2015 *)

PROG

(MAGMA) a0:=2; a1:=7; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013

CROSSREFS

Cf. A000032. A000045.

Sequence in context: A020894 A165995 A267212 * A041643 A041395 A042345

Adjacent sequences:  A022110 A022111 A022112 * A022114 A022115 A022116

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 23 20:33 EDT 2017. Contains 283965 sequences.