A280749 - OEIS

%I #13 Dec 04 2018 07:43:43

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

%T 1,0,1,0,0,0,1,0,1,0,3,0,0,0,2,0,2,0,2,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,

%U 2,0,0,0,1,0,1,0,2,0,0,0,1,0,1,0,1,0,0,0,3,0,0,0,2,0,0,0,2,0,2,0,2

%N One of a set of five sequences arising in the enumeration of optimal {0,1,-1}-configurations.

%C Normally only the bisection of this sequence would be entered (since every second term is zero), but we make an exception here because it is part of a set. (The bisection is A280748.)

%H Peter J. Grabner and Clemens Heuberger, <a href="https://doi.org/10.1007/s10623-005-6158-y">On the number of optimal base 2 representations of integers</a>, Des. Codes Cryptogr. 40 (2006), no. 1, 25-39.

%H S. Kropf, S. Wagner, <a href="https://arxiv.org/abs/1605.03654">q-Quasiadditive functions</a>, arXiv:1605.03654 [math.CO], 2016.

%F See Maple code for the five recurrences.

%p for p from 1 to 5 do u[p][0]:=1; od;

%p u[1][1]:=1; u[2][1]:=1; u[3][1]:=0; u[4][1]:=0; u[5][1]:=0;

%p for n from 2 to 100 do

%p if n mod 2 = 0 then

%p u[1][n]:=u[1][n/2]; u[2][n]:=u[1][n/2]; u[3][n]:=u[2][n/2]; u[4][n]:=u[1][n/2]; u[5][n]:=u[4][n/2];

%p else

%p u[1][n]:=u[2][(n-1)/2]+u[4][(n+1)/2]; u[2][n]:=u[3][(n-1)/2]; u[3][n]:=0; u[4][n]:=u[5][(n-1)/2]; u[5][n]:=0;

%p fi;

%p od:

%p [seq(u[1][n],n=0..100)]; # A280747

%p [seq(u[2][n],n=0..100)]; # A280748

%p [seq(u[3][n],n=0..100)]; # A280749

%p [seq(u[4][n],n=0..100)]; # A280750

%p [seq(u[5][n],n=0..100)]; # A280751

%t (* See A280747 *)

%Y Cf. A280747, A280748, A280750, A280751.

%K nonn

%O 0,13

%A _N. J. A. Sloane_, Jan 14 2017