OFFSET
0,2
COMMENTS
Original name was: Generalized Jacobsthal numbers.
Sums of rows of the triangle in A109225. - Reinhard Zumkeller, Jun 23 2005
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).
FORMULA
a(n) = 2^(n+2)/3 - (-1)^n/12 - (2*n+1)/4.
G.f: (2*x^3 - x^2 - x + 1)/( (x+1)*(1-2*x)*(1-x)^2).
a(n+2) = a(n+1) + 2*a(n) + n, a(0)=0, a(1)=2.
a(n+1) = 2*a(n) + floor(n/2). Franklin T. Adams-Watters, Oct 17 2013
a(n)+a(n+1) = A095768(n+1). - R. J. Mathar, Apr 15 2024
MATHEMATICA
LinearRecurrence[{3, -1, -3, 2}, {1, 2, 4, 9}, 40] (* Harvey P. Dale, Nov 13 2013 *)
PROG
(Magma) [2^(n+2)/3-(-1)^n/12-(2*n+1)/4: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 18 2003
STATUS
approved