OFFSET
0,3
COMMENTS
a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6,7,8,9} avoiding 01 and 02. - Milan Janjic, Dec 17 2015
LINKS
Robert Israel, Table of n, a(n) for n = 0..990
Index entries for linear recurrences with constant coefficients, signature (10, -2).
FORMULA
a(n) = ((5+sqrt(23))^n-(5-sqrt(23))^n)/(2*sqrt(23)).
G.f.: x/(1-10*x+2*x^2). - Robert Israel, Dec 17 2015
MAPLE
f:= gfun:-rectoproc({a(n) = 10*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Dec 17 2015
MATHEMATICA
LinearRecurrence[{10, -2}, {0, 1}, 50] (* T. D. Noe, May 23 2011 *)
PROG
(Magma) I:=[0, 1]; [n le 2 select I[n] else 10*Self(n-1)-2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015
(PARI) concat(0, Vec(x/(1-10*x+2*x^2) + O(x^100))) \\ Altug Alkan, Dec 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rolf Pleisch, May 22 2011
EXTENSIONS
Corrected and extended by T. D. Noe, May 23 2011
STATUS
approved