cp's OEIS Frontend

A369924 Number of uniform words of length n with adjacent elements unequal using an infinite alphabet up to permutations of the alphabet.

%I A369924 #12 Mar 29 2025 03:26:28
%S A369924 1,1,1,1,2,1,7,1,38,30,331,1,5560,1,47846,164585,815693,1,35149698,1,
%T A369924 338596631,4420377702,4939227217,1,1430570927009,66218360626,
%U A369924 2850860253242,372419004321831,628358300200811,1,156433852692766134,1,2606291948338277064
%N A369924 Number of uniform words of length n with adjacent elements unequal using an infinite alphabet up to permutations of the alphabet.
%C A369924 A word is uniform here if each symbol that occurs in the word occurs with the same frequency.
%C A369924 a(n) is the number of ways to partition [n] into parts of equal size and no part containing values that differ by 1.
%H A369924 Andrew Howroyd, <a href="/A369924/b369924.txt">Table of n, a(n) for n = 0..200</a>
%F A369924 a(n) = Sum_{d|n} A322013(d, n/d) for n > 0.
%F A369924 a(p) = 1 for prime p.
%e A369924 The a(4) = 2 words are abab, abcd.
%e A369924 The a(6) = 7 words are ababab, abacbc, abcabc, abcacb, abcbac, abcbca, abcdef.
%e A369924 The a(4) = 2 set partitions are {{1,3}, {2,4}} and {{1},{2},{3},{4}}.
%o A369924 (PARI) \\ Needs T(n,k) from A322013.
%o A369924 a(n) = {if(n==0, 1, sumdiv(n, d, T(d, n/d)))}
%Y A369924 The case for adjacent elements possibly equal is A038041.
%Y A369924 Cf. A322013, A369925 (circular words).
%K A369924 nonn
%O A369924 0,5
%A A369924 _Andrew Howroyd_, Feb 06 2024