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A138003
Binomial transform of 1, 1, 0, -1, -1 (periodically continued).
4
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
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
FORMULA
From R. J. Mathar, May 02 2008: (Start)
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). (End)
MATHEMATICA
LinearRecurrence[{3, -4, 2, -1}, {1, 2, 3, 3}, 50] (* Paolo Xausa, Dec 05 2023 *)
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 * A329232 A057682 A124841
KEYWORD
sign,easy
AUTHOR
Paul Curtz, May 01 2008
EXTENSIONS
Edited by R. J. Mathar, May 02 2008
STATUS
approved