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A280750 One of a set of five sequences arising in the enumeration of optimal {0,1,-1}-configurations. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
LINKS
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
Sequence in context: A024363 A050600 A129691 * A280748 A117454 A115357
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 14 2017
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)