OFFSET
0,2
COMMENTS
For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6,7,8} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7,8} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
a(n) is the number of compositions of n when there are 7 types of each natural number. - Milan Janjic, Aug 13 2010
For n>0, a(n) is not the sum of two nonnegative cubes. - Bruno Berselli, Mar 20 2012
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
F. Conti, R. Dvornicich, T. Franzoni and S. Mortola, Il Fibonacci N. 0 (included in Il Fibonacci, Unione Matematica Italiana, 2011), 1990, Problem 0.12.4 (see Berselli's comment).
LINKS
Vincenzo Librandi, 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 (8).
FORMULA
G.f.: (1-x)/(1-8*x).
G.f.: 1/( 1 - 7*Sum_{k>=1} x^k ).
a(n) = 7*8^(n-1); a(0)=1.
a(n) = 8*a(n-1) + (-1)^n * C(1, 1-n).
a(n) = 7*Sum_{k=0..n-1} a(k), for n>=1. - Adi Dani, Jun 24 2011
E.g.f.: (1 + 7*exp(8*x))/8. - G. C. Greubel, Mar 16 2020
MAPLE
1, seq(7*8^(n-1), n=1..20); # G. C. Greubel, Mar 16 2020
MATHEMATICA
q = 8; Join[{a = 1}, Table[If[n == 0, a = q*a - 1, a = q*a], {n, 0, 25}]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
PROG
(PARI) my(x='x+O('x^66)); Vec((1-x)/(1-8*x)) /* Joerg Arndt, Jun 25 2011 */
(Magma) [1] cat [7*8^(n-1): n in [1..20]]; // G. C. Greubel, Mar 16 2020
(Sage) [1]+[7*8^(n-1) for n in (1..20)] # G. C. Greubel, Mar 16 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, May 28 2000
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved