A099858 A Chebyshev transform of (1+3x)/(1-3x).

1, 6, 17, 42, 109, 288, 755, 1974, 5167, 13530, 35423, 92736, 242785, 635622, 1664081, 4356618, 11405773, 29860704, 78176339, 204668310, 535828591, 1402817466, 3672623807, 9615053952, 25172538049, 65902560198, 172535142545

Offset

0,2

Comments

The g.f. is related to the g.f. of A099856 by the Chebyshev mapping G(x)-> (1/(1+x^2))G(x/(1+x^2)).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,3,-1).

Formula

G.f.: (1+3x+x^2)/((1+x^2)(1-3x+x^2)); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*(6*3^(n-2k-1)-0^(n-2k)}; a(n)=sum{k=0..n, (0^k+6*Fib(2k))cos(pi*(n-k)/2)}; a(n)=sum{k=0..n, A099857(k)*cos(pi*(n-k)/2)}; a(n)=3a(n-1)-2a(n-2)+3a(n-3)-a(n-4).

(1/2) [4Fib(2n+2) - I^n - (-I)^n ]. - Ralf Stephan, Dec 04 2004

Mathematica

LinearRecurrence[{3, -2, 3, -1}, {1, 6, 17, 42}, 40] (* Harvey P. Dale, Apr 17 2024 *)

Crossrefs

Sequence in context: A343518 A365409 A171507 * A232567 A062020 A066183

Adjacent sequences: A099855 A099856 A099857 * A099859 A099860 A099861

Keyword

easy,nonn

Author

Paul Barry, Oct 28 2004

Status

approved