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.

A214945 Number of squarefree words of length 6 in an (n+1)-ary alphabet.

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%I A214945 #9 Jul 22 2018 08:44:44
%S A214945 0,42,696,4260,16680,50190,126672,281736,569520,1068210,1886280,
%T A214945 3169452,5108376,7947030,11991840,17621520,25297632,35575866,49118040,
%U A214945 66704820,89249160,117810462,153609456,198043800,252704400,319392450,400137192
%N A214945 Number of squarefree words of length 6 in an (n+1)-ary alphabet.
%C A214945 Row 6 of A214943.
%H A214945 R. H. Hardin, <a href="/A214945/b214945.txt">Table of n, a(n) for n = 1..210</a>
%F A214945 Empirical: a(n) = n^6 + n^5 - 3*n^4 - 2*n^3 + 2*n^2 + n.
%F A214945 Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F A214945 G.f.: 6*x^2*(7 + 67*x + 45*x^2 + x^3) / (1 - x)^7.
%F A214945 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A214945 (End)
%e A214945 Some solutions for n=2:
%e A214945 ..0....1....1....1....0....1....2....0....1....2....0....2....0....1....0....2
%e A214945 ..2....0....0....2....1....0....1....2....2....1....1....1....1....2....2....0
%e A214945 ..0....2....1....1....2....2....0....1....0....2....0....2....2....1....0....2
%e A214945 ..1....1....2....0....0....1....1....0....2....0....2....0....1....0....1....1
%e A214945 ..2....0....0....2....2....2....2....2....1....1....1....1....0....1....0....2
%e A214945 ..1....1....1....1....1....0....0....0....0....0....0....2....1....2....2....0
%Y A214945 Cf. A214943.
%K A214945 nonn
%O A214945 1,2
%A A214945 _R. H. Hardin_, Jul 30 2012