A242536 Number of n-length words on {1,2,3,4} such that the maximal runs of identical odd integers are of odd length and the maximal runs of identical even integers are of even length.

1, 2, 4, 12, 26, 66, 160, 386, 946, 2292, 5582, 13578, 33016, 80330, 195370, 475236, 1155974, 2811762, 6839416, 16636178, 40466002, 98429844, 239421374, 582370554, 1416562360, 3445657082, 8381242522, 20386597380, 49588514390, 120619477410, 293395730296

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,3,2,-2)

Formula

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

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

Example

a(3)=12 because we have: 111, 122, 131, 144, 221, 223, 313, 322, 333, 344, 441, 443.

Mathematica

n=4; 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]

Crossrefs

Cf. A062200, A242510, A242537.

Sequence in context: A236002 A291406 A219752 * A027132 A148172 A148173

Adjacent sequences: A242533 A242534 A242535 * A242537 A242538 A242539

Keyword

nonn,easy

Author

Geoffrey Critzer, May 17 2014

Status

approved