OFFSET
0,2
COMMENTS
For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11} 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 10*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover Publications, N.Y., 1964, pp. 194-196.
LINKS
FORMULA
a(n) = 11*a(n-1) + (-1)^n*C(2,2-n).
G.f.: (1-x)^2/(1-11*x).
a(n) = Sum_{k=0..n} A201780(n,k)*9^k. - Philippe Deléham, Dec 05 2011
From Elmo R. Oliveira, Jun 13 2026: (Start)
a(n) = 11*a(n-1) for n > 2.
E.g.f.: (21 - 11*x + 100*exp(11*x))/121. (End)
EXAMPLE
G.f. = 1 + 9*x + 100*x^2 + 1100*x^3 + 12100*x^4 + 133100*x^5 + ... - Michael Somos, Jun 14 2026
MATHEMATICA
Join[{1, 9}, 100*11^Range[0, 20]] (* Harvey P. Dale, May 24 2012 *)
(* Alternative: *)
Join[{1, 9}, NestList[11#&, 100, 20]] (* Harvey P. Dale, May 24 2012 *)
PROG
(PARI) {a(n) = polcoeff( (1 - x)^2 / (1 - 11*x) + x*O(x^n), n)}; /* Michael Somos, Jun 14 2026 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jun 18 2000
EXTENSIONS
More terms from James Sellers, Jul 04 2000
More terms from Elmo R. Oliveira, Jun 13 2026
STATUS
approved