A056002 a(n) = (10^2)*11^(n-2); a(0)=1, a(1)=9.

1, 9, 100, 1100, 12100, 133100, 1464100, 16105100, 177156100, 1948717100, 21435888100, 235794769100, 2593742460100, 28531167061100, 313842837672100, 3452271214393100, 37974983358324100, 417724816941565100

Offset: 0

Author

Barry E. Williams, Jun 18 2000

Keywords

• easy
• nonn

Comments

For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007

a(n) is the number of generalized compositions of n when there are 10*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Crossrefs

Cf. A001020.

Programs

Mathematica

Join[{1,9},100*11^Range[0,20]] (* or *) Join[{1,9},NestList[11#&,100,20]] (* Harvey P. Dale, May 24 2012 *)

Formula

a(n)=11a(n-1)+[(-1)^n]*C(2, 2-n). G.f.(x)=(1-x)^2/(1-11x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*9^k. - Philippe Deléham, Dec 05 2011

Extensions

More terms from James Sellers, Jul 04 2000