A055995 a(n) = 64*9^(n-2), a(0)=1, a(1)=7.

1, 7, 64, 576, 5184, 46656, 419904, 3779136, 34012224, 306110016, 2754990144, 24794911296, 223154201664, 2008387814976, 18075490334784, 162679413013056, 1464114717117504, 13177032454057536, 118593292086517824

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} 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} 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 8*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 (9)

Crossrefs

Second differences of 9^n (A001019). Cf. A055275.

Formula

a(n) = 9a(n-1) + ((-1)^n)*C(2, 2-n).

G.f.: (1-x)^2/(1-9x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*7^k. - Philippe Deléham, Dec 05 2011