OFFSET
0,2
COMMENTS
For n >= 2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7} 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} 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 6*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. 122-125, 194-196.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (7).
FORMULA
a(n) = 6^2 * 7^(n-2), n >= 2 with a(0)=1, a(1)=5.
G.f.: (1-x)^2/(1-7*x).
a(n) = Sum_{k=0..n} A201780(n,k)*5^k. - Philippe Deléham, Dec 05 2011
E.g.f.: (13 - 7*x + 36*exp(7*x))/49. - G. C. Greubel, Mar 16 2020
MAPLE
MATHEMATICA
Join[{1, 5}, NestList[7#&, 36, 20]] (* Harvey P. Dale, Sep 04 2017 *)
PROG
(Magma) [1, 5] cat [36*7^(n-2): n in [2..30]]; // G. C. Greubel, Mar 16 2020
(Sage) [1, 5]+[36*7^(n-2) for n in (2..30)] # G. C. Greubel, Mar 16 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, May 10 2000
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Mar 16 2020
STATUS
approved