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
a(n) = 8*F(n) + F(n-3) for F = A000045. - J. M. Bergot, Jul 14 2017
a(n) = Fibonacci(n+4) + Lucas(n-1). - Greg Dresden and Henry Sauer, Mar 04 2022
E.g.f.: 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 6*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Jul 18 2022
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 *)
LinearRecurrence[{1, 1}, {2, 7}, 37] (* or *)
CoefficientList[Series[-(5 x + 2)/(x^2 + x - 1), {x, 0, 36}], x] (* Michael De Vlieger, Jul 14 2017 *)
PROG
(Magma) a0:=2; a1:=7; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013
(PARI) a(n)=8*fibonacci(n)+fibonacci(n-3) \\ Charles R Greathouse IV, Jul 14 2017
(PARI) a(n)=([0, 1; 1, 1]^n*[2; 7])[1, 1] \\ Charles R Greathouse IV, Jul 14 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved