0,2

Number of aa-avoiding words of length n on the alphabet {a,b,c,d}.

Index entries for sequences related to linear recurrences with constant coefficients

Joerg Arndt, Fxtbook

Tanya Khovanova, Recursive Sequences

G.f.=(1+z)/(1-3z-3z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007

a(n) = (5*sqrt(21)/42 + 1/2)*(3/2 + sqrt(21)/2))^(n-1) + (-5*sqrt(21)/42 + 1/2)*(3/2 - sqrt(21)/2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 20 2008

a[0]:=1: a[1]:=4: for n from 2 to 27 do a[n]:=3*a[n-1]+3*a[n-2] od: seq(a[n], n=0..27); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007

#include <iostream.h> #include <stdlib.h> #include <math.h> int main(int argc, char *argv[]) { int i; // counter for for loop double j; // for (i=1; i < 12; i++) // change 9 to whatever number you want if desired { j = ( 5.0*sqrt(21.0)/42 + 1.0/2.0)*pow((3.0/2.0 + sqrt(21)/2), (i-1))+ (-5.0*sqrt(21.0)/42 + 1.0/2.0)*pow((3.0/2.0 - sqrt(21)/2), (i-1)) ; // cout << i << ' ' << j << " "; } return EXIT_SUCCESS; } - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 20 2008

Cf. A028859 = a(n+2) = 2 a(n+1) + 2 a(n); A086347 = On a 3 X 3 board, number of n-move routes of chess king ending at a given side cell. a(n) = 4a(n-1) + 4a(n-2).

Cf. A128235.

Sequence in context: A131497 A077823 A047108 this_sequence A095930 A026850 A109642

Adjacent sequences: A125142 A125143 A125144 this_sequence A125146 A125147 A125148

nonn

Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007