A272501 Number of n-letter strings over a ten letter alphabet where no letter appears exactly three times.

1, 10, 100, 990, 9640, 91900, 855100, 7754050, 68545360, 592095160, 5020469200, 42054532750, 350538754600, 2926602465940, 24587635740040, 208406304739450, 1784567064858400, 15453880256710000, 135459380264937760, 1202295227210127910, 10804306958861721400

Offset

0,2

Comments

species is SEQ_10(SET_(!=3)(Z))

Links

Table of n, a(n) for n=0..20.

Math Stackexchange, Marko Riedel et al., N digit numbers with no digit appearing exactly twice.

Formula

E.g.f.: (exp(z)-z^3/3!)^10.

Example

a(3) = 10^3-10 because all 3-letter strings qualify except the strings containing only one type of letter.

Maple

a := n->n!*coeftayl((exp(z)-z^3/3!)^10, z=0, n);

Mathematica

With[{nn=20}, CoefficientList[Series[(Exp[x]-x^3/3!)^10, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Apr 08 2019 *)

Crossrefs

Cf. A265325, A272502, A272503.

Sequence in context: A334612 A125948 A121084 * A171284 A125897 A182979

Adjacent sequences: A272498 A272499 A272500 * A272502 A272503 A272504

Keyword

nonn,base

Author

Marko Riedel, May 01 2016

Status

approved