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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

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*(6*3^(n-2*k-1)-0^(n-2*k)).

a(n) = Sum_{k=0..n} (0^k+6*Fibonacci(2*k))*cos(Pi*(n-k)/2).

a(n) = Sum_{k=0..n} A099857(k)*cos(Pi*(n-k)/2).

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

a(n) = (1/2)*(4*Fibonacci(2*n+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

Cf. A099856, A099857.

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

URL: https://oeis.org/A099858

⇱ A099858 - OEIS