The number of ways to color n balls in a row with 3 colors with no color runs having lengths greater than 4. This sequence is a special case of the general problem for coloring n balls in a row with p colors where each color has a given maximum run-length. In this example, the bounds are uniformly 4. It can be phrased in terms of tossing a p-faced die n times, requiring each face to have no runs longer than b.

A181140

The number of ways to color n balls in a row with 3 colors with no color runs having lengths greater than 4. This sequence is a special case of the general problem for coloring n balls in a row with p colors where each color has a given maximum run-length. In this example, the bounds are uniformly 4. It can be phrased in terms of tossing a p-faced die n times, requiring each face to have no runs longer than b.

Terms

    a(0) =3a(1) =9a(2) =27a(3) =81a(4) =240a(5) =714a(6) =2124a(7) =6318a(8) =18792a(9) =55896a(10) =166260a(11) =494532a(12) =1470960a(13) =4375296a(14) =13014096a(15) =38709768a(16) =115140240a(17) =342478800a(18) =1018685808a(19) =3030029232a(20) =9012668160a(21) =26807724000a(22) =79738214400a(23) =237177271584a(24) =705471756288

External references