OFFSET
0,1
COMMENTS
REFERENCES
G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chap. 4, Sect. 1, Problem 148.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).
FORMULA
a(n) = (2^(floor(n/2) + 2 + (-1)^n) + (-1)^floor(n/2)) / 3.
From Colin Barker, Apr 05 2013: (Start)
a(n) = a(n-2) + 2*a(n-4);
g.f.: (2*x^2+x+3) / ((1+x^2)*(1-2*x^2)). (End)
MATHEMATICA
LinearRecurrence[{0, 1, 0, 2}, {3, 1, 5, 1}, 50] (* Harvey P. Dale, Dec 31 2017 *)
PROG
(Magma) [(2^(Floor(n/2) + 2 + (-1)^n) + (-1)^Floor(n/2)) / 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
(PARI) m=50; v=concat([3, 1, 5, 1], vector(m-4)); for(n=5, m, v[n]=v[n-2] +2*v[n-4]); v \\ G. C. Greubel, Nov 08 2018
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Aug 27 2005
EXTENSIONS
a(22) corrected by Vincenzo Librandi, Aug 17 2011
STATUS
approved