OFFSET
0,2
COMMENTS
Number of (s(0), s(1), ..., s(n+1)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n+1, s(0) = 1, s(n+1) = 2. - Herbert Kociemba, Jun 17 2004
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4).
FORMULA
a(n) = (3*2^(n+1) - sqrt(3)*(1-sqrt(3))^(n+1) + sqrt(3)*(1+sqrt(3))^(n+1))/12. - Herbert Kociemba, Jun 17 2004
2*a(n) = 2^n + A002605(n+1). - R. J. Mathar, Sep 11 2019
a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3). - Wesley Ivan Hurt, May 14 2021
PROG
(PARI) Vec((1-2*x-x^2)/(1-4*x+2*x^2+4*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved