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 (5,-7,3).
FORMULA
a(n) = (5*3^n)/12 + n/2 - 3/4.
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3). - Colin Barker, Jan 15 2015
G.f.: x*(x^2 + x - 1) / ((x-1)^2*(3*x-1)). - Colin Barker, Jan 15 2015
EXAMPLE
S -> AD | DA | BE | EB | CF, D-> BC, E -> AC, F -> AB | BA, A -> a, B -> b, C -> c; so a(3)=12.
MATHEMATICA
a[n_] := (15*3^n)/36 + n/2 - 3/4; Table[ a[n], {n, 1, 26}] (* Robert G. Wilson v, Jan 29 2004 *)
PROG
(PARI) Vec(x*(x^2+x-1)/((x-1)^2*(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 29 2004
STATUS
approved