A327804 - OEIS

%I #6 Sep 26 2019 08:07:06

%S 0,1,1,1,1,2,1,1,1,1,2,1,1,2,1,1,1,1,1,3,2,3,1,1,1,1,2,1,1,2,1,1,1,1,

%T 1,2,1,1,3,2,2,2,3,1,1,2,1,1,1,1,1,3,2,3,1,1,1,1,2,1,1,2,1,1,1,1,1,2,

%U 1,1,2,1,1,1,1,4,3,5,2,2,2,2,2,5,3,4,1,1,1,1,2

%N Leading coefficient of the n-th Stern polynomial.

%H A. Schinzel, <a href="https://doi.org/10.1007/978-3-319-28203-9_25">The leading coefficients of Stern polynomials</a>, in: From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz (J. Sander et al., eds.), Springer, 2016, 427-434.

%t B[0, _] = 0; B[1, _] = 1; B[n_, t_] := B[n, t] = If[EvenQ[n], t B[n/2, t], B[1 + (n-1)/2, t] + B[(n-1)/2, t]];

%t a[n_] := Coefficient[B[n, t], t, Exponent[B[n, t], t]]; a[0] = 0;

%t a /@ Range[0, 90] (* _Jean-François Alcover_, Sep 26 2019, from A125184 *)

%o (PARI) pol(n) = {if (n<2, return (n)); if (n%2, pol((n+1)/2) + pol((n-1)/2), x*pol(n/2));}

%o a(n) = my(p=pol(n)); if (p==0, 0, polcoef(p, poldegree(p)));

%Y Cf. A125184, A277314, A277315.

%K nonn

%O 0,6

%A _Michel Marcus_, Sep 26 2019