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A362030
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Irregular triangle read by rows where row n contains the balanced binary words of length 2n interpreted as binary numbers.
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6
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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, ...;
...
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MAPLE
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T:= n-> sort(map(Bits[Join], combinat[permute]([0$n, 1$n])))[]:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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