

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
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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^2x+1)/(x^42*x^3+4*x^23*x+1). a(n)=5a(n1)10a(n2)+10a(n3)5a(n4)+2a(n5). a(n)=3a(n1)4a(n2)+2a(n3)a(n4).  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[#a1]+2*a[#a2]a[#a3])); a \\ Charles R Greathouse IV, Jun 02 2011


CROSSREFS

Cf. A129929.
Sequence in context: A193382 A106242 A121474 * A329232 A057682 A124841
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



