A240954 Number of initially rising meander words, where each letter of the cyclic n-ary alphabet occurs three times.

1, 0, 1, 29, 100, 182, 484, 902, 2116, 4034, 8836, 17138, 36100, 70850, 145924, 288578, 586756

Offset

0,4

Comments

In a meander word letters of neighboring positions have to be neighbors in the alphabet, where in a cyclic alphabet the first and the last letters are considered neighbors too. The words are not considered cyclic here.

A word is initially rising if it is empty or if it begins with the first letter of the alphabet that can only be followed by the second letter in this word position.

a(n) is also the number of (3*n-1)-step walks on n-dimensional cubic lattice from (1,0,...,0) to (3,3,...,3) with positive unit steps in all dimensions such that the indices of dimensions used in consecutive steps differ by 1 or are in the set {1,n}.

Links

Table of n, a(n) for n=0..16.

Formula

a(2n) = A169721(n) for n>1.

Example

a(0) = 1: the empty word.
a(1) = 0 = |{ }|.
a(2) = 1 = |{ababab}|.
a(3) = 29 = |{ababcacbc, ababcbcac, abacabcbc, abacacbcb, abacbacbc, abacbcabc, abacbcacb, abacbcbac, abacbcbca, abcabacbc, abcabcabc, abcabcacb, abcabcbac, abcabcbca, abcacabcb, abcacbabc, abcacbacb, abcacbcab, abcacbcba, abcbabcac, abcbacabc, abcbacacb, abcbacbac, abcbacbca, abcbcabac, abcbcabca, abcbcacab, abcbcacba, abcbcbaca}|.

Crossrefs

Row n=3 of A209349.

Sequence in context: A138625 A154405 A092373 * A087641 A161665 A127464

Adjacent sequences: A240951 A240952 A240953 * A240955 A240956 A240957

Keyword

nonn,walk,more

Author

Alois P. Heinz, Aug 04 2014

Status

approved