OFFSET
1,2
COMMENTS
Each row contains contains its successor as a proper subsequence.
Note that this supposes that the Thue-Morse sequence A010059 has offset 1, whereas the true offset is 0. So really the entries should all be reduced by 1. - N. J. A. Sloane, Jul 01 2016
Apparently T(n,3) = A004119(n+1) for n>0. Apparently T(n,4) = A083575(n) for n>0. - R. J. Mathar, Nov 06 2018
EXAMPLE
Northwest corner, n>=0, k>=1:
1 4 6 7 10 11 13 16 18 19
1 4 7 11 13 16 19 21 25 28
1 7 13 21 25 31 37 41 49 55
1 13 25 41 49 61 73 81 97 109
1 25 49 81 97 121 145 161 193 217
1 49 97 161 193 241 289 321 385 433
1 97 193 321 385 481 577 641 769 865
The Thue-Morse sequence A010059 begins with 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, from which we see that the first 4 terms (=1,0,0,1) occur at positions 1, 7, 13, ..., as indicated for row n=2.
MAPLE
A010060 := proc(n)
local i;
add(i, i=convert(n, base, 2)) mod 2 ;
end proc:
A010059 := proc(n)
1-A010060(n) ;
end proc:
A248416Off0 := proc(n, k)
option remember ;
local strtN, binpat, src, thue ;
if k = 1 then
strtN := 0 ;
else
strtN := 1+procname(n, k-1) ;
end if;
binpat := [seq(A010059(i), i=0..n-1)] ;
for src from strtN do
thue := [seq(A010059(i), i=src..src+nops(binpat)-1)] ;
if binpat=thue then
return src ;
end if;
end do:
end proc:
A248416 := proc(n, k)
1+A248416Off0(2^n, k) ;
end proc:
for d from 1 to 11 do
for k from d to 1 by -1 do
printf("%d, ", A248416(d-k, k)) ;
end do: # R. J. Mathar, Nov 06 2018
MATHEMATICA
z = 3000; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 20]; Length[u]
t[p_, q_] := t[p, q] = Table[u[[k]], {k, p, q}];
r[n_] := Select[Range[z], t[#, # + 2^(n - 1)] == t[1, 1 + 2^(n - 1)] &]
TableForm[Table[r[n], {n, 0, 10}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Oct 06 2014
EXTENSIONS
Definitions and examples clarified. - R. J. Mathar, Nov 06 2018
STATUS
approved