A280750 - OEIS

A280750

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

1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 3, 0, 2, 2, 2, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 3, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 4, 0, 3, 3, 3, 0, 2, 0, 2, 0, 2, 2, 4, 0, 2

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OFFSET

0,7

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, A280749, A280751.

Sequence in context: A024363 A050600 A129691 * A280748 A117454 A115357

Adjacent sequences: A280747 A280748 A280749 * A280751 A280752 A280753

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 14 2017

STATUS

approved