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A138003 Binomial transform of 1, 1, 0, -1, -1 (periodically continued). 3
1, 2, 3, 3, 0, -8, -21, -34, -34, 0, 89, 233, 377, 377, 0, -987, -2584, -4181, -4181, 0, 10946, 28657, 46368, 46368, 0, -121393, -317811, -514229, -514229, 0, 1346269, 3524578, 5702887, 5702887, 0, -14930352, -39088169, -63245986, -63245986 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Shares many elements with A103311, as already indicated by the similarity of the two generating functions. First differences are essentially in A105371. - R. J. Mathar, May 02 2008

The longer of the two recurrences ensures that the sequence (like A133476) equals its 5th differences. - R. J. Mathar, May 02 2008

LINKS

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (3,-4,2,-1).

FORMULA

O.g.f.:(x^2-x+1)/(x^4-2*x^3+4*x^2-3*x+1). a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5). a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4). - R. J. Mathar, May 02 2008

PROG

(PARI) a=[1, 2, 3, 3]; for(i=1, 99, a=concat(a, 3*a[#a]-4*a[#a-1]+2*a[#a-2]-a[#a-3])); a \\ Charles R Greathouse IV, Jun 02 2011

CROSSREFS

Cf. A129929.

Sequence in context: A193382 A106242 A121474 * A057682 A124841 A085355

Adjacent sequences:  A138000 A138001 A138002 * A138004 A138005 A138006

KEYWORD

sign,easy

AUTHOR

Paul Curtz, May 01 2008

EXTENSIONS

Edited by R. J. Mathar, May 02 2008

STATUS

approved

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Last modified July 20 05:37 EDT 2019. Contains 325168 sequences. (Running on oeis4.)