A367912 - OEIS

%I #12 Dec 28 2023 09:22:07

%S 1,1,1,1,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2,2,4,4,4,4,2,2,2,2,4,4,4,4,2,2,

%T 2,2,4,4,4,4,2,2,2,2,4,4,4,4,4,4,4,4,7,7,7,7,4,4,4,4,7,7,7,7,3,3,3,3,

%U 5,5,5,5,3,3,3,3,5,5,5,5,5,5,5,5,8,8,8,8

%N Number of multisets that can be obtained by choosing a binary index of each binary index of n.

%C A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.

%C The run-lengths are all 4 or 8.

%e The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with multiset choices {1,1,2}, {1,1,3}, {1,2,2}, {1,2,3}, {1,3,3}, {2,2,3}, {2,3,3}, so a(52) = 7.

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]],1];

%t Table[Length[Union[Sort/@Tuples[bpe/@bpe[n]]]], {n,0,100}]

%Y Positions of ones are A253317.

%Y The version for multisets and divisors is A355733, for sequences A355731.

%Y The version for multisets is A355744, for sequences A355741.

%Y For a sequence of distinct choices we have A367905, firsts A367910.

%Y Positions of first appearances are A367913, sorted A367915.

%Y Choosing a sequence instead of multiset gives A368109, firsts A368111.

%Y Choosing a set instead of multiset gives A368183, firsts A368184.

%Y A048793 lists binary indices, length A000120, sum A029931.

%Y A058891 counts set-systems, covering A003465, connected A323818.

%Y A070939 gives length of binary expansion.

%Y A096111 gives product of binary indices.

%Y Cf. A072639, A309326, A326031, A326702, A326753, A355735, A355739, A355740, A355745, A367771, A367906.

%K nonn

%O 0,5

%A _Gus Wiseman_, Dec 12 2023