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A100063 A Chebyshev transform of Jacobsthal numbers. 6
1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A Chebyshev transform of A001045(n+1): if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))*A(x/(1+x^2)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).

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

FORMULA

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

a(n) = n*Sum_{k=0..floor(n/2)} binomial(n-k, k)(-1)^k*A001045(n-2k+1)/(n-k).

Multiplicative with a(3^e) = 2, a(p^e) = 1 otherwise. - David W. Wilson, Jun 11 2005

Dirichlet g.f.: zeta(s)*(1+1/3^s). Dirichlet convolution of A154272 and A000012. - R. J. Mathar, Feb 07 2011

a(n) = 2 if n == 0 (mod 3) and n > 0, and a(n) = 1 otherwise. - Amiram Eldar, Nov 01 2022

MATHEMATICA

PadRight[{1}, 120, {2, 1, 1}] (* or *) LinearRecurrence[{0, 0, 1}, {1, 1, 1, 2}, 120] (* Harvey P. Dale, Jul 08 2015 *)

PROG

(PARI) my(x='x+O('x^50)); Vec((1+x)(1+x^2)/(1-x^3)) \\ G. C. Greubel, May 03 2017

CROSSREFS

Cf. A000012, A100051, A061347, A057079, A154272.

Sequence in context: A281727 A122876 A131713 * A057079 A132419 A131556

Adjacent sequences: A100060 A100061 A100062 * A100064 A100065 A100066

KEYWORD

easy,nonn,mult

AUTHOR

Paul Barry, Nov 02 2004

STATUS

approved

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Last modified December 3 11:24 EST 2022. Contains 358517 sequences. (Running on oeis4.)