A190869 a(n) = 10*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1.

0, 1, 10, 98, 960, 9404, 92120, 902392, 8839680, 86592016, 848240800, 8309223968, 81395758080, 797339132864, 7810599812480, 76511319859072, 749491998965760, 7341897349939456, 71919989501463040, 704516100314751488, 6901321024144588800, 67604178040816385024

Offset: 0

Author

Rolf Pleisch, May 22 2011

Keywords

• nonn
• easy

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).

Programs

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

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 *)

PARI

concat(0, Vec(x/(1-10*x+2*x^2) + O(x^100))) \\ Altug Alkan, Dec 17 2015

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

Extensions

Corrected and extended by T. D. Noe, May 23 2011