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

1, 0, 3, 3, 21, 63, 243, 969, 3657, 12987, 43959, 143685, 458109, 1435047, 4439451, 13612257, 41474577, 125798643, 380343519, 1147320285, 3455328261, 10394294175, 31242648963, 93853773369, 281825558361, 846030320043, 2539248584583, 7620161669109

Offset: 0

Author

Geoffrey Critzer, Mar 20 2012

Keywords

• nonn
• easy

Examples

			a(2)=3 because we have (letting our alphabet be {0,1,2}) three length two sequences: (0,0), (1,1), (2,2).
a(3)=3 because we have: (0,0,0), (1,1,1), (2,2,2).
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Crossrefs

Cf. A130102.

Programs

Mathematica

nn=20; a=Exp[x]-x; Range[0,nn]! CoefficientList[Series[a^3, {x,0,nn}], x]
LinearRecurrence[{10,-40,82,-91,52,-12},{1,0,3,3,21,63,243,969,3657,12987},30] (* Harvey P. Dale, Aug 20 2015 *)

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

Formula

E.g.f.: (exp(x)-x)^3.

For n>3: a(n) = 3^n - 3*n*2^(n-1) + 3*n*(n-1).

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