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A022355 Fibonacci sequence beginning 0, 21. 3
0, 21, 21, 42, 63, 105, 168, 273, 441, 714, 1155, 1869, 3024, 4893, 7917, 12810, 20727, 33537, 54264, 87801, 142065, 229866, 371931, 601797, 973728, 1575525, 2549253, 4124778, 6674031, 10798809, 17472840, 28271649, 45744489, 74016138, 119760627, 193776765 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
G.f.: 21*x/(1 - x - x^2). - Philippe Deléham, Nov 20 2008
a(n) = 21*Fibonacci(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=8, k=2. - Bruno Berselli, Feb 20 2017
From Colin Barker, Feb 20 2017: (Start)
a(n) = -21*(((1-sqrt(5))/2)^n - ((1+sqrt(5))/2)^n) / sqrt(5).
a(n) = a(n-1) + a(n-2) for n>1.
(End)
MATHEMATICA
LinearRecurrence[{1, 1}, {0, 21}, 30] (* Harvey P. Dale, Dec 13 2014 *)
PROG
(PARI) concat(0, Vec(21*x/(1 - x - x^2) + O(x^50))) \\ Colin Barker, Feb 20 2017
CROSSREFS
Cf. A000045.
Sequence in context: A158772 A151910 A040421 * A371100 A048245 A246034
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)