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A240954
Number of initially rising meander words, where each letter of the cyclic n-ary alphabet occurs three times.
1
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}.
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
KEYWORD
nonn,walk,more
AUTHOR
Alois P. Heinz, Aug 04 2014
STATUS
approved