A391564 - OEIS

%I #16 Dec 14 2025 19:32:51

%S 1,-1,1,1,0,-1,3,-1,1,0,-1,1,1,-3,5,1,1,-1,1,0,-1,1,-1,-1,5,-1,1,3,1,

%T -5,11,-1,3,-1,0,1,1,-1,1,0,-1,1,-1,-1,0,1,-3,1,9,-5,3,1,-1,-1,5,-3,7,

%U -1,-1,5,3,-11,21,1,5,-3,1,1,-1,0,1,-1,3,-1,0,1,1,-1,1,0,-1,1,-1,-1,0,1,-3,1,-1,0,1,-1,-1,3

%N Numerator of the constant term of the remainder obtained when Stern polynomial B(n,x) is divided by B(5,x).

%H Antti Karttunen, <a href="/A391564/b391564.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o memo_for_ps = Map();

%o ps(n) = if(n<2, n, my(v); if(mapisdefined(memo_for_ps,n,&v), v, v = if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)); if(n%2, mapput(memo_for_ps,n,v)); (v)));

%o A391564(n) = numerator(polcoef((ps(n) % ps(5)), 0));

%Y Cf. A391565 (denominators), A391566 (positions of 0's).

%Y Cf. A125184, A186891, A260443 for a description of Stern polynomials.

%K sign,frac,look

%O 1,7

%A _Antti Karttunen_, Dec 14 2025