OFFSET
0,3
COMMENTS
Equals triangle A173284 * [1, 2, 3, ...]. - Gary W. Adamson, Mar 03 2010
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-3,1,1).
FORMULA
a(n) = A054450(n+2, 2).
G.f.: Fib(x)/(1-x^2)^2, with Fib(x)=1/(1-x-x^2) = g.f. A000045 (Fibonacci numbers without 0).
a(n-2) = Fibonacci(n+1) - binomial(n-floor(n/2), floor(n/2)), or a(n-2) = Sum_{i=0..floor(n/2)-1} binomial(n-i, i). - Jon Perry, Mar 18 2004
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+2, k). - Paul Barry, Oct 23 2004
MAPLE
BB:=1/(1-k^2)^2/(1-k-k^2): seq(coeff(series(BB, k, n+1), k, n), n=0..50); # Zerinvary Lajos, May 16 2007
MATHEMATICA
LinearRecurrence[{1, 3, -2, -3, 1, 1}, {1, 1, 4, 5, 12, 17}, 40] (* Harvey P. Dale, Oct 06 2024 *)
PROG
(PARI) Vec(-1/((x-1)^2*(x+1)^2*(x^2+x-1)) + O(x^100)) \\ Colin Barker, Jun 14 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wolfdieter Lang, Apr 27 2000
EXTENSIONS
More terms from James A. Sellers, Apr 28 2000
STATUS
approved