A242510 Number of n-length words on {1,2,3} such that the maximal blocks (runs) of 1's have odd length, the maximal blocks of 2's have even length and the maximal blocks of 3's have odd length.

1, 2, 3, 8, 15, 32, 67, 138, 289, 600, 1249, 2600, 5409, 11258, 23427, 48752, 101455, 211128, 439363, 914322, 1902721, 3959600, 8240001, 17147600, 35684481, 74260082, 154536643, 321593688, 669242575, 1392706512, 2898248707

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (1,2,1,-1).

Formula

G.f.: (1 + x - x^2)/(1 - x - 2*x^2 - x^3 +x^4).

a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4). - Fung Lam, May 18 2014

Example

a(3)=8 because we have: 111, 122, 131, 221, 223, 313, 322, 333.

Mathematica

n=3; nn=30; CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i]), {i, 1, n}])/.Join[Table[v[i]->z/(1-z^2), {i, 1, n, 2}], Table[v[i]->z^2/(1-z^2), {i, 2, n, 2}]], {z, 0, nn}], z]
(* Changing n=3 at the beginning of this code to n = k, (for k a positive integer) will return the number of n-length words on {1, 2, ..., k} where the maximal run lengths of odd integers are odd and the maximal run lengths of even integers are even. *)

Crossrefs

Cf. A062200, A242536, A242537.

Sequence in context: A195095 A331829 A166920 * A080206 A132862 A055543

Adjacent sequences: A242507 A242508 A242509 * A242511 A242512 A242513

Keyword

nonn

Author

Geoffrey Critzer, May 16 2014

Status

approved