A242537 - OEIS

A242537

Number of n-length words on {1,2,3,4,5} 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, 3, 8, 27, 82, 255, 794, 2463, 7654, 23775, 73850, 229407, 712606, 2213583, 6876098, 21359343, 66348934, 206100927, 640215146, 1988712255, 6177573934, 19189513071, 59608742162, 185163746895, 575177598550, 1786684895967, 5550012597050, 17240107585311, 53553267556606, 166353513271311, 516747019188962

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OFFSET

0,2

LINKS

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

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

FORMULA

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

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

EXAMPLE

a(3)=27 because we have: 111, 122, 131, 135, 144, 151, 153, 221, 223, 225, 313, 315, 322, 333, 344, 351, 353, 441, 443, 445, 513, 515, 522, 531, 535, 544, 555.

MATHEMATICA

n=5; 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, A242536.

Sequence in context: A332833 A148823 A205503 * A323795 A148824 A148825

Adjacent sequences: A242534 A242535 A242536 * A242538 A242539 A242540

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, May 17 2014

STATUS

approved