A055846 a(n) = 25*6^(n-2), with a(0)=1 and a(1)=4.

1, 4, 25, 150, 900, 5400, 32400, 194400, 1166400, 6998400, 41990400, 251942400, 1511654400, 9069926400, 54419558400, 326517350400, 1959104102400, 11754624614400, 70527747686400, 423166486118400, 2538998916710400

Offset: 0

Author

Barry E. Williams, Jun 03 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} 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} 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 5*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 (6)

Crossrefs

First differences of A052934. Cf. A000400.

Programs

Mathematica

LinearRecurrence[{6},{1,4,25},30] (* Harvey P. Dale, May 25 2023 *)

Formula

a(n) = 25*6^(n-2), a(0)=1, a(1)=4. a(n) = 6a(n-1) + ((-1)^n)*binomial(2, 2-n); g.f.(x)=(1-x)^2/(1-6x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*4^k. - Philippe Deléham, Dec 05 2011

Extensions

More terms from James Sellers, Jun 05 2000