OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-4).
FORMULA
a(n) - a(n-1) = A081631(n-2).
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3).
G.f.: x*(1 + x + 2*x^2) / ((x-1)*(2*x+1)*(2*x-1)). - R. J. Mathar, Apr 30 2010
a(n) = 2^n - A084247(n-1). - Bruno Berselli, Sep 15 2011
MATHEMATICA
a[1] := 1;
a[n_] := a[n] = a[n - 1]/2 + Sqrt[(5 + 4*(-1)^(n - 1))]/2:
Table[2^(n - 1)*a[n], {n, 1, 30}]
PROG
(PARI) a(n)=(3<<(n+1)-(-2)^n)\/6-1 \\ Charles R Greathouse IV, Sep 14 2011
(Magma) [(3*2^(n+1)-8-(-2)^n)/6:n in [1..40]]; // Vincenzo Librandi, Sep 15 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Apr 29 2010
STATUS
approved