OFFSET
0,3
COMMENTS
We call chen(n) = 1 / a(n) if a(n) != 0 and otherwise 0, the Chen sequence, after Kwang-Wu Chen (see link). Note how this sequence is used in the computation of the Swiss-Knife polynomials A153641.
LINKS
Winston de Greef, Table of n, a(n) for n = 0..6603
Kwang-Wu Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Sequences, 4 (2001), #01.1.6.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,-4).
MAPLE
a := n -> if irem(n + 1, 4) = 0 then 0 else (-1)^iquo(n + 1, 4) * 2^iquo(n, 2) fi:
seq(a(n), n = 0..49);
# Alternative:
gf := (2*x^2 + x + 1)/(4*x^4 + 1): ser := series(gf, x, 24):
seq(coeff(ser, x, n), n = 0..20);
MATHEMATICA
A363524list[nmax_]:=LinearRecurrence[{0, 0, 0, -4}, {1, 1, 2, 0}, nmax+1]; A363524list[100] (* Paolo Xausa, Aug 06 2023 *)
PROG
(SageMath)
def a(n): return 0 if 4.divides(n + 1) else (-1)^((n + 1) // 4) * 2^(n // 2)
print([a(n) for n in range(45)])
(PARI) a(n)=if(n % 4 == 3, 0, (-1)^((n + 1) \ 4) * 2^(n \ 2)) \\ Winston de Greef, Jun 30 2023
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Peter Luschny, Jun 17 2023
STATUS
approved