login
A362030
Irregular triangle read by rows where row n contains the balanced binary words of length 2n interpreted as binary numbers.
6
1, 2, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 135
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
Columns k=1-2 give: A000225, A083329.
Row sums give A131568.
Main diagonal gives A036563(n+1).
Cf. A000984 (row lengths), A072601, A072603, A368804 (binary).
Sequence in context: A189224 A018762 A059746 * A024620 A232527 A188375
KEYWORD
nonn,tabf,easy
AUTHOR
Louis Conover, Apr 05 2023
STATUS
approved