login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A022410 a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=3, a(1)=11. 1
3, 11, 15, 27, 43, 71, 115, 187, 303, 491, 795, 1287, 2083, 3371, 5455, 8827, 14283, 23111, 37395, 60507, 97903, 158411, 256315, 414727, 671043, 1085771, 1756815, 2842587, 4599403, 7441991, 12041395, 19483387, 31524783, 51008171, 82532955, 133541127 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
From R. J. Mathar, Mar 11 2011: (Start)
a(n+1) - a(n) = A156279(n).
G.f.: (3 + 5*x - 7*x^2) / ((x - 1)*(x^2 + x - 1)).
(End)
a(n) = A156279(n+1) - 1. - Bruno Berselli, Jul 27 2017
From Colin Barker, Jul 27 2017: (Start)
a(n) = 2^(-n)*(-2^n + 2*(1-sqrt(5))^(1+n) + 2*(1+sqrt(5))^(1+n)).
a(n) = 2*a(n-1) - a(n-3) for n>2.
(End)
MATHEMATICA
LinearRecurrence[{2, 0, -1}, {3, 11, 15}, 40] (* Bruno Berselli, Jul 27 2017 *)
PROG
(Python)
from sympy import lucas
def a(n): return 4 * lucas(n + 1) - 1
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 27 2017
(PARI) Vec((3+5*x-7*x^2)/((x-1)*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Jul 27 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3+5*x-7*x^2)/((x-1)*(x^2+x-1)))); // G. C. Greubel, Feb 28 2018
CROSSREFS
Sequence in context: A186302 A323103 A046159 * A146254 A039503 A276971
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 18 01:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)