A280749 - OEIS

A280749

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

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, 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, 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

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OFFSET

0,13

COMMENTS

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.)

LINKS

Table of n, a(n) for n=0..100.

Peter J. Grabner and Clemens Heuberger, On the number of optimal base 2 representations of integers, Des. Codes Cryptogr. 40 (2006), no. 1, 25-39.

S. Kropf, S. Wagner, q-Quasiadditive functions, arXiv:1605.03654 [math.CO], 2016.

FORMULA

See Maple code for the five recurrences.

MAPLE

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

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

for n from 2 to 100 do

if n mod 2 = 0 then

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];