A109629 - OEIS

%I #23 May 02 2024 17:30:05

%S 0,1,1,-4,12,-28,52,-80,112,-176,376,-976,2536,-6112,13504,-27456,

%T 51552,-89344,142240,-206656,274800,-354240,546976,-1283648,3918800,

%U -12104064,34744256,-92031104,227231104,-528840704,1170706304,-2481880320,5062828736,-9967712256

%N Sequence of Mahler coefficients of the Gray code function.

%D 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.

%H Alois P. Heinz, <a href="/A109629/b109629.txt">Table of n, a(n) for n = 0..1000</a>

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

%p g:= proc(n) option remember; `if`(n<2, n,

%p       (b-> b+g(2*b-1-n))(2^ilog2(n)))

%p     end:

%p a:= n-> add((-1)^(n-k)*binomial(n, k)*g(k), k=0..n):

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Oct 09 2008

%t g[n_] := BitXor[n, Quotient[n, 2]];

%t a[n_] := Sum[(-1)^(n-k) Binomial[n, k] g[k], {k, 0, n}];

%t a /@ Range[0, 40] (* _Jean-François Alcover_, Nov 18 2020 *)

%Y Cf. A003188, A372304.

%K sign

%O 0,4

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

%E More terms from _Alois P. Heinz_, Oct 09 2008