OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
P. R. J. Asveld, Generating all permutations by context-free grammars in Chomsky normal form, Theoretical Computer Science 354 (2006) 118-130.
Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
FORMULA
a(n) = ceiling[ (5*3^(n-2))/2 + 2^(n-1) - 1/2 ] for n > 1.
G.f.: -x*(2*x^3-2*x^2-2*x+1) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 15 2015
a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n >= 5. - Robert Israel, Jan 15 2015
EXAMPLE
S -> AD | DA | BE | EB, D -> BC | CB, E -> AC | CA, A -> a, B -> b, C-> c; so a(3)=11.
MAPLE
f:= gfun:-rectoproc({a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3), a(1)=1, a(2)=4, a(3)=11, a(4)=30}, a(n), 'remember'):
seq(f(n), n=1..100); # Robert Israel, Jan 15 2015
MATHEMATICA
f[n_] := Ceiling[5/2*3^(n - 2) + 2^(n - 1) - 1/2]; Table[ f[n], {n, 2, 27}] (* Robert G. Wilson v, Jan 30 2004 *)
PROG
(PARI) Vec(-x*(2*x^3-2*x^2-2*x+1)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jan 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter R. J. Asveld, Jan 27 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jan 30 2004
STATUS
approved