A242510 -id:A242510 - cp's OEIS frontend

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

Geoffrey Critzer, May 17 2014

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

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

Cf. A062200, A242510, A242537.

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]

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

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.

Original entry on oeis.org

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

Offset: 0

Geoffrey Critzer, May 17 2014

			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.

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

Cf. A062200, A242510, A242536.

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]

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

cp's OEIS Frontend

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.

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