OFFSET
1,2
COMMENTS
Within a row, strings are ordered lexicographically, which means the resulting values are ordered numerically.
This is from an idea of David Lovler, which he calls "zigzags". It is a rearrangement of A072601. A072603 lists all the numbers that are not in this sequence. A000984 gives the number of coin flip sequences of length 2,4,6, etc.
Not a permutation of the integers. E.g. 8 never occurs. When there are more 0's than 1's, adding 0's doesn't bring it to balance. - Kevin Ryde, Aug 31 2023
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..17576 (rows 1..8 of the triangle, flattened).
EXAMPLE
The first few terms written as binary words with leading 0's: 01, 10, 0011, 0101, 0110, 1001, 1010, 1100, 000111, 001011, 001101, 001110, ... (cf. A368804).
Triangle T(n,k) begins:
1, 2;
3, 5, 6, 9, 10, 12;
7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, ...;
15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, ...;
...
MAPLE
T:= n-> sort(map(Bits[Join], combinat[permute]([0$n, 1$n])))[]:
seq(T(n), n=1..4); # Alois P. Heinz, Apr 13 2023
MATHEMATICA
T[n_] := Sort[FromDigits[#, 2] & /@ Permutations[Join[ConstantArray[0, n], ConstantArray[1, n]]]]; Flatten[Table[T[n], {n, 1, 4}]][[1 ;; 64]] (* Robert P. P. McKone, Aug 29 2023 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Louis Conover, Apr 05 2023
STATUS
approved