OFFSET
0,3
COMMENTS
a(2n) - a(2n-1) = Fibonacci(2n+1).
Diagonal sums of triangle A054450. - Paul Barry, Oct 23 2004
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Donatella Merlini, Massimo Nocentini, Algebraic Generating Functions for Languages Avoiding Riordan Patterns, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.3.
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2).
FORMULA
a(n) = Sum_{j=0..floor(n/2)} Sum_{i=0..j} binomial(n-j, i).
a(n) = Fibonacci(n+3) - 2^floor((n+1)/2). - Vladeta Jovovic, Feb 12 2003
G.f.: (1-x^2)/((1-x-x^2)(1-2x^2)). - Paul Barry, Jan 13 2005
MAPLE
with (combinat):a[0]:=0:a[1]:=1:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] od: seq(a[n], n=1..31); # Zerinvary Lajos, Mar 17 2008
MATHEMATICA
CoefficientList[Series[(1 - x^2) / ((1 - x - x^2) (1 - 2 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{1, 3, -2, -2}, {1, 1, 3, 4}, 40] (* Harvey P. Dale, Nov 30 2018 *)
PROG
(Magma) [Fibonacci(n+3)-2^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 05 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 08 2003
STATUS
approved