cp's OEIS Frontend

A362030 Irregular triangle read by rows where row n contains the balanced binary words of length 2n interpreted as binary numbers.

%I A362030 #46 Jan 09 2024 10:28:26
%S A362030 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,
%T A362030 50,52,56,15,23,27,29,30,39,43,45,46,51,53,54,57,58,60,71,75,77,78,83,
%U A362030 85,86,89,90,92,99,101,102,105,106,108,113,114,116,120,135
%N A362030 Irregular triangle read by rows where row n contains the balanced binary words of length 2n interpreted as binary numbers.
%C A362030 Within a row, strings are ordered lexicographically, which means the resulting values are ordered numerically.
%C A362030 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.
%C A362030 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
%H A362030 Paolo Xausa, <a href="/A362030/b362030.txt">Table of n, a(n) for n = 1..17576</a> (rows 1..8 of the triangle, flattened).
%e A362030 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).
%e A362030 Triangle T(n,k) begins:
%e A362030    1,  2;
%e A362030    3,  5,  6,  9, 10, 12;
%e A362030    7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, ...;
%e A362030   15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, ...;
%e A362030   ...
%p A362030 T:= n-> sort(map(Bits[Join], combinat[permute]([0$n, 1$n])))[]:
%p A362030 seq(T(n), n=1..4);  # _Alois P. Heinz_, Apr 13 2023
%t A362030 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 *)
%Y A362030 Columns k=1-2 give: A000225, A083329.
%Y A362030 Row sums give A131568.
%Y A362030 Main diagonal gives A036563(n+1).
%Y A362030 Cf. A000984 (row lengths), A072601, A072603, A368804 (binary).
%K A362030 nonn,tabf,easy
%O A362030 1,2
%A A362030 _Louis Conover_, Apr 05 2023