OFFSET
0,2
COMMENTS
Given a first row 1/A026741(k+1), k >= 0, of an array, namely
1/1, 1/1, 1/3, 1/2, 1/5, 1/3, 1/7, ...,
the next row generated by the Akiyama-Tanigawa transform is
0, 4/3, -1/2, 6/5, -2/3, 8/7, -3/4, 10/9, -4/5, 12/11, -5/6, 14/13, ...
The current sequence contains the numerators of these fractions; the denominators are A026741(n+2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Merlini, R. Sprugnoli, M. C. Verri, The Akiyama-Tanigawa Transformation, Integers, 5 (1) (2005) #A05.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(n) = +2*a(n-2) -a(n-4).
a(n) = (1/4)*(n + 6 - 3*(-1)^n*(n + 2)).
G.f.: x*(4 - x - 2*x^2) / ( (1-x)^2*(1+x)^2 ).
E.g.f.: (1/4)*((6+x)*exp(x) - 3*(2-x)*exp(-x)). - G. C. Greubel, Dec 04 2022
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {0, 4, -1, 6}, 60] (* G. C. Greubel, Dec 04 2022 *)
PROG
(Magma) [(1/4)*(n+6 -3*(-1)^n*(n+2)): n in [0..50]]; // G. C. Greubel, Dec 04 2022
(SageMath) [(1/4)*(n + 6 - 3*(-1)^n*(n + 2)) for n in range(51)] # G. C. Greubel, Dec 04 2022
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Curtz, Mar 18 2010
STATUS
approved