A099517 A transform of (1-x)/(1-2x).

1, 1, 2, 3, 6, 10, 17, 27, 44, 71, 116, 188, 305, 493, 798, 1291, 2090, 3382, 5473, 8855, 14328, 23183, 37512, 60696, 98209, 158905, 257114, 416019, 673134, 1089154, 1762289, 2851443, 4613732, 7465175, 12078908, 19544084, 31622993, 51167077

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• nonn

Comments

A transform of A011782 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3))

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,0,-1).

Crossrefs

Cf. A099505, A099508, A099516, A000071.

Formula

G.f.: (1-x+x^3)/((1+x^3)*(1-2*x+x^3)).

a(n) = 2*a(n-1)-2*a(n-3)+2*a(n-4)-a(n-6).

a(n) = sum{k=0..floor(n/3), binomial(n-2*k, k)*(-1)^k*(2^(n-3*k)+0^(n-3*k))/2}.

a(n) = A057079(n+1)/6 +A000045(n+3)/2 -A010694(n)/6. - R. J. Mathar, Sep 21 2012