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A327804
Leading coefficient of the n-th Stern polynomial.
0
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, 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, 1, 1, 2, 1, 1, 1, 1, 4, 3, 5, 2, 2, 2, 2, 2, 5, 3, 4, 1, 1, 1, 1, 2
OFFSET
0,6
LINKS
A. Schinzel, The leading coefficients of Stern polynomials, in: From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz (J. Sander et al., eds.), Springer, 2016, 427-434.
MATHEMATICA
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]];
a[n_] := Coefficient[B[n, t], t, Exponent[B[n, t], t]]; a[0] = 0;
a /@ Range[0, 90] (* Jean-François Alcover, Sep 26 2019, from A125184 *)
PROG
(PARI) pol(n) = {if (n<2, return (n)); if (n%2, pol((n+1)/2) + pol((n-1)/2), x*pol(n/2)); }
a(n) = my(p=pol(n)); if (p==0, 0, polcoef(p, poldegree(p)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Sep 26 2019
STATUS
approved