A218130 Number of length 6 primitive (=aperiodic or period 6) n-ary words.

0, 0, 54, 696, 4020, 15480, 46410, 117264, 261576, 530640, 998910, 1770120, 2984124, 4824456, 7526610, 11387040, 16772880, 24132384, 34006086, 47038680, 63991620, 85756440, 113368794, 148023216, 191088600, 244124400, 308897550, 387400104, 481867596, 594798120

Offset: 0

Author

Alois P. Heinz, Oct 21 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Row n=6 of A143324.

Programs

Maple

a:= n-> (((n^3-1)*n-1)*n+1)*n:
seq(a(n), n=0..30);

Mathematica

Table[n^6-n^3-n^2+n,{n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,54,696,4020,15480,46410},30] (* Harvey P. Dale, Oct 13 2017 *)

Formula

G.f.: -6*x^2*(9+53*x+47*x^2+11*x^3)/(x-1)^7.

a(n) = n^6-n^3-n^2+n.