A055847 a(0)=1, a(1)=6, a(n)=49*8^(n-2) if n>=2.

1, 6, 49, 392, 3136, 25088, 200704, 1605632, 12845056, 102760448, 822083584, 6576668672, 52613349376, 420906795008, 3367254360064, 26938034880512, 215504279044096, 1724034232352768, 13792273858822144, 110338190870577152

Offset: 0

Author

Barry E. Williams, Jun 03 2000

Keywords

• nonn
• easy

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} 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} 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 7*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 (8).

Crossrefs

First differences of A055274. Cf. A001018.

Programs

Mathematica

Join[{1,6},NestList[8#&,49,20]] (* Harvey P. Dale, Dec 08 2013 *)

Formula

a(n) = 8*a(n-1) + (-1)^n*C(2, 2-n).

G.f.: (1-x)^2/(1-8*x).

a(n) = sum_{k, 0<=k<=n} A201780(n,k)*6^k. - Philippe Deléham, Dec 05 2011

Extensions

More terms from James Sellers, Jun 05 2000