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

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];
else
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;
fi;
od:
[seq(u[1][n], n=0..100)]; # A280747
[seq(u[2][n], n=0..100)]; # A280748
[seq(u[3][n], n=0..100)]; # A280749
[seq(u[4][n], n=0..100)]; # A280750
[seq(u[5][n], n=0..100)]; # A280751

Mathematica

(* See A280747 *)

Crossrefs

Cf. A280747, A280748, A280750, A280751.

Sequence in context: A361561 A081212 A280751 * A321936 A085491 A321013

Adjacent sequences: A280746 A280747 A280748 * A280750 A280751 A280752

Keyword

nonn

Author

N. J. A. Sloane, Jan 14 2017

Status

approved