cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A355255 Irregular table read by rows: a(n,k) gives the number of distinct necklaces that appear in the following procedure: starting with the n-bead, (0,1)-necklace given by k written in binary, repeatedly take the first differences (mod 2) of the beads. 0 <= k < 2^n.

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%I A355255 #18 Jul 05 2022 23:19:27
%S A355255 1,1,2,1,3,3,2,1,2,2,1,2,1,1,2,1,5,5,4,5,3,4,5,5,4,3,5,4,5,5,2,1,4,4,
%T A355255 3,4,3,3,4,4,3,3,4,3,4,4,3,4,3,3,4,3,4,4,3,3,4,4,3,4,3,3,2,1,4,4,3,4,
%U A355255 2,3,3,4,2,2,4,3,4,3,2,4,2,2,4,2,3,4,3,3,4,4,1,3,3,2,4,4,3,2,3,2,4,4,2,2,4,3,3,4,1,3,4,3,3,4,2,4,3,1,4,3,2,3,4,2,4,4,2
%N A355255 Irregular table read by rows: a(n,k) gives the number of distinct necklaces that appear in the following procedure: starting with the n-bead, (0,1)-necklace given by k written in binary, repeatedly take the first differences (mod 2) of the beads. 0 <= k < 2^n.
%C A355255 For j >= 1, the sequence a(j,1) begins
%C A355255 2, 3, 2, 5, 4, 4, 8, 9, 8, 8, 32, 8, 64, 16, 16, 17, 16, 16, 512, 16, 64, 64, 2048, 16, 1024, 128, 512, 32, 16384, 32, ...
%C A355255 Conjecture: a(2^m,1) = 2^m + 1 for all m > 1.
%C A355255 Conjecture: a(m,1) is a power of 2 whenever m is not a power of 2.
%C A355255 The sequence of the number of distinct values in the n-th row begins 1, 2, 3, 2, 5, 4, 4, 4, 9, 4, 8, 4, 8, 4, 10, 6, 17, 6, 10, ... - _Peter Kagey_, Jul 03 2022
%H A355255 Peter Kagey, <a href="/A355255/b355255.txt">Rows n = 0..12 of the triangle, flattened</a>
%e A355255 Table begins:
%e A355255 n\k | 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
%e A355255 ----+-----------------------------------------------
%e A355255   0 | 1;
%e A355255   1 | 1, 2;
%e A355255   2 | 1, 3, 3, 2;
%e A355255   3 | 1, 2, 2, 1, 2, 1, 1, 2;
%e A355255   4 | 1, 5, 5, 4, 5, 3, 4, 5, 5, 4, 3, 5, 4, 5, 5, 2;
%e A355255 ... | ...
%e A355255 a(5,13) = 4 because 13 is 01101 in binary; the sequence of first differences is 01101, 10111, 11000, 01001, 11011, ...; and 10111 is the same necklace as 11011.
%Y A355255 Cf. A038556, A334594.
%K A355255 nonn,tabf,base,look
%O A355255 0,3
%A A355255 _Peter Kagey_, Jun 26 2022