A109629 Sequence of Mahler coefficients of the Gray code function.

0, 1, 1, -4, 12, -28, 52, -80, 112, -176, 376, -976, 2536, -6112, 13504, -27456, 51552, -89344, 142240, -206656, 274800, -354240, 546976, -1283648, 3918800, -12104064, 34744256, -92031104, 227231104, -528840704, 1170706304, -2481880320, 5062828736, -9967712256

Offset

0,4

References

F. Clarke, The Gray code function, in: p-adic methods and their applications, A.J. Baker and R. J. Plymen editors, Oxford University Press, New York 1992, 1-7.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} (-1)^{n-k} * C(n,k) * g(k), where g is the Gray code function A003188.

Maple

g:= proc(n) option remember; `if`(n<2, n,
      (b-> b+g(2*b-1-n))(2^ilog2(n)))
    end:
a:= n-> add((-1)^(n-k)*binomial(n, k)*g(k), k=0..n):
seq(a(n), n=0..40);  # Alois P. Heinz, Oct 09 2008

Mathematica

g[n_] := BitXor[n, Quotient[n, 2]];
a[n_] := Sum[(-1)^(n-k) Binomial[n, k] g[k], {k, 0, n}];
a /@ Range[0, 40] (* Jean-François Alcover, Nov 18 2020 *)

Crossrefs

Cf. A003188, A372304.

Sequence in context: A278211 A342235 A192736 * A112087 A166019 A184633

Adjacent sequences: A109626 A109627 A109628 * A109630 A109631 A109632

Keyword

sign

Author

Jan-Christoph Schlage-Puchta (jcp(AT)math.uni-freiburg.de), Aug 02 2005

Extensions

More terms from Alois P. Heinz, Oct 09 2008

Status

approved