A209183 Number of words, either empty or beginning with the first letter of the cyclic 4-ary alphabet, where each letter of the alphabet occurs n times and letters of neighboring word positions are equal or neighbors in the alphabet.

1, 2, 62, 2830, 151686, 8893482, 552309938, 35702836038, 2377145582550, 161906392007554, 11227409430866262, 790011772823243214, 56264746328351077194, 4048156319577916177530, 293797748889879887735802, 21483000387938509658756790, 1581177100760460768472276086

Offset: 0

Author

Alois P. Heinz, Mar 05 2012

Keywords

• nonn
• walk

Comments

The first and the last letters are considered neighbors in a cyclic alphabet. The words are not considered cyclic here.

a(n) is also the number of (4*n-1)-step walks on 4-dimensional cubic lattice from (1,0,0,0) to (n,n,n,n) with positive unit steps in all dimensions such that the indices of dimensions used in consecutive steps differ by less than 2 or are in the set {1,4}.

Crossrefs

Column k=4 of A208879.