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.

A209528 The number of length n ternary sequences in which no symbol appears exactly once.

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%I A209528 #25 Aug 20 2015 18:57:31
%S A209528 1,0,3,3,21,63,243,969,3657,12987,43959,143685,458109,1435047,4439451,
%T A209528 13612257,41474577,125798643,380343519,1147320285,3455328261,
%U A209528 10394294175,31242648963,93853773369,281825558361,846030320043,2539248584583,7620161669109
%N A209528 The number of length n ternary sequences in which no symbol appears exactly once.
%H A209528 Colin Barker, <a href="/A209528/b209528.txt">Table of n, a(n) for n = 0..1000</a>
%H A209528 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,82,-91,52,-12).
%F A209528 E.g.f.: (exp(x)-x)^3.
%F A209528 For n>3: a(n) = 3^n - 3*n*2^(n-1) + 3*n*(n-1).
%F A209528 G.f.: -(72*x^9 -312*x^8 +546*x^7 -492*x^6 +325*x^5 -202*x^4 +109*x^3 -43*x^2 +10*x -1) / ((x -1)^3*(2*x -1)^2*(3*x -1)). - _Colin Barker_, Nov 30 2014
%e A209528 a(2)=3 because we have (letting our alphabet be {0,1,2}) three length two sequences: (0,0), (1,1), (2,2).
%e A209528 a(3)=3 because we have: (0,0,0), (1,1,1), (2,2,2).
%t A209528 nn=20; a=Exp[x]-x; Range[0,nn]! CoefficientList[Series[a^3, {x,0,nn}], x]
%t A209528 LinearRecurrence[{10,-40,82,-91,52,-12},{1,0,3,3,21,63,243,969,3657,12987},30] (* _Harvey P. Dale_, Aug 20 2015 *)
%o A209528 (PARI) Vec(-(72*x^9 -312*x^8 +546*x^7 -492*x^6 +325*x^5 -202*x^4 +109*x^3 -43*x^2 +10*x -1) / ((x -1)^3*(2*x -1)^2*(3*x -1)) + O(x^100)) \\ _Colin Barker_, Nov 30 2014
%Y A209528 Cf. A130102.
%K A209528 nonn,easy
%O A209528 0,3
%A A209528 _Geoffrey Critzer_, Mar 20 2012