OFFSET
1,3
REFERENCES
M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 37. [From N. J. A. Sloane, Jan 29 2009]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
I. Nemes et al., How to do Monthly problems with your computer, Amer. Math. Monthly, 104 (1997), 505-519.
Index entries for linear recurrences with constant coefficients, signature (2,-1,2).
FORMULA
a(n) = 2^(n-1) + cos(n*Pi/2).
a(n) = sum(2^k*C(n-k, 2k)*n/(n-k), k=0..floor(n/3)).
a(n) = ((-i)^n+i^n+2^n)/2, where i=sqrt(-1). a(n) = 2*a(n-1)-a(n-2)+2*a(n-3). G.f.: x*(1-x+3*x^2)/((1-2*x)*(1+x^2)). [Colin Barker, May 08 2012]
MAPLE
f:=n->2^(n-1)+cos(Pi*n/2);
MATHEMATICA
CoefficientList[Series[(1-x+3*x^2)/((1-2*x)*(1+x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, May 09 2012 *)
Table[Which[Mod[n, 4]==0, 2^(n-1)+1, Mod[n, 4]==2, 2^(n-1)-1, True, 2^(n-1)], {n, 30}] (* or *) LinearRecurrence[{2, -1, 2}, {1, 1, 4}, 30] (* Harvey P. Dale, May 01 2018 *)
PROG
(Magma) I:=[1, 1, 4]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, May 09 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, R. K. Guy, Simon Plouffe.
STATUS
approved