A055996 a(n) = 81*10^(n-2), a(0)=1, a(1)=8.

1, 8, 81, 810, 8100, 81000, 810000, 8100000, 81000000, 810000000, 8100000000, 81000000000, 810000000000, 8100000000000, 81000000000000, 810000000000000, 8100000000000000, 81000000000000000, 810000000000000000

Offset: 0

Author

Barry E. Williams, Jun 04 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} 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} 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 9*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
• Index entries for linear recurrences with constant coefficients, signature (10)

Crossrefs

Second differences of 10^n (A011557). Cf. A052268.

Programs

Mathematica

Join[{1,8},NestList[10#&,81,20]] (* Harvey P. Dale, Nov 20 2015 *)

Formula

a(n)=10a(n-1)+[(-1)^n]*C(2, 2-n). G.f.(x)=(1-x)^2/(1-10x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*8^k. - Philippe Deléham, Dec 05 2011