OFFSET
2,1
COMMENTS
Triangle read by rows in which row n lists the binary numbers with n digits and with some initial repeats, n >= 2.
Also triangle read by rows in which row n lists the binary words of length n with some initial repeats and with initial digit 1, n >= 2.
LINKS
EXAMPLE
Triangle begins, starting at row 2:
11;
110, 111;
1010, 1100, 1101, 1110, 1111;
10100, 10101, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111;
MAPLE
s:= proc(n) s(n):= `if`(n=1, [[1]], map(x->
[[x[], 0], [x[], 1]][], s(n-1))) end:
T:= proc(n) map(x-> parse(cat(x[])), select(proc(l) local i;
for i to iquo(nops(l), 2) do if l[1..i]=l[i+1..2*i]
then return true fi od; false end, s(n)))[] end:
seq(T(n), n=2..7); # Alois P. Heinz, Dec 04 2012
MATHEMATICA
T[n_] := FromDigits /@ Select[Range[2^(n-1), 2^n-1] // IntegerDigits[#, 2]&, FindTransientRepeat[Reverse[#], 2][[2]] != {}&];
Table[T[n], {n, 2, 7}] // Flatten (* Jean-François Alcover, Feb 12 2025 *)
CROSSREFS
KEYWORD
nonn,tabf,base,changed
AUTHOR
Omar E. Pol, Dec 03 2012
STATUS
approved