OFFSET
0,4
COMMENTS
Transform of the Jacobsthal numbers by the Chebyshev related transform which maps g(x) -> (1/(1-x^2))*g(x/(1-x^2)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-1,-1).
FORMULA
MATHEMATICA
LinearRecurrence[{1, 4, -1, -1}, {0, 1, 1, 5}, 40] (* G. C. Greubel, Jan 14 2022 *)
PROG
(Sage) [sum(binomial(n-k, k)*lucas_number1(n-2*k, 1, -2) for k in (0..(n/2))) for n in (0..40)] # G. C. Greubel, Jan 14 2022
(Magma)
J:= func< n | (2^n - (-1)^n)/3 >; // A001045
[(&+[Binomial(n-k, k)*J(n-2*k): k in [0..Floor(n/2)]]) : n in [0..40]]; // _G. C. Greubel, Jan 14 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 14 2005
STATUS
approved