A242495 Number of length n words on {1,2,3,4} with at most one consecutive 1 and at most two consecutive 2's and at most three consecutive 3's and at most four consecutive 4's.

1, 4, 15, 56, 208, 773, 2872, 10672, 39655, 147350, 547523, 2034486, 7559742, 28090486, 104378617, 387850022, 1441172953, 5355109869, 19898515060, 73938894118, 274742112508, 1020886629235, 3793410119173, 14095551768590

Offset

0,2

Comments

Column k=4 of A242464.

Links

Fung Lam, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2 )*(1 + x + x^2 + x^3 + x^4)/(1 - x - 5*x^2 - 12*x^3 - 18*x^4 - 22*x^5 - 20*x^6 - 15*x^7 - 8*x^8 - 3*x^9). (corrected by Fung Lam, May 18 2014)

Example

a(3) = 56 because there are 64 length 3 words on {1,2,3,4} but we don't count 111, 112, 113, 114, 211, 222, 311, or 411.

Mathematica

nn=23; CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i])/.v[i]->(z-z^(i+1))/(1-z), {i, 1, 4}]), {z, 0, nn}], z]

Crossrefs

Cf. A242452.

Sequence in context: A291030 A217779 A191606 * A221859 A106707 A125905

Adjacent sequences: A242492 A242493 A242494 * A242496 A242497 A242498

Keyword

nonn,easy

Author

Geoffrey Critzer, May 16 2014

Status

approved