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A209353
Number of initially rising meander words, where each letter of the cyclic 7-ary alphabet occurs n times.
1
1, 1, 19, 902, 53636, 3771698, 292587922, 24422343208, 2150227555324, 197404215493922, 18735386882618558, 1827242795963079380, 182291530666463403220, 18537924237935355619360
OFFSET
0,3
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 (7*n-1)-step walks on 7-dimensional cubic lattice from (1,0,...,0) to (n,n,...,n) 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 {1,7}.
EXAMPLE
a(0) = 1: the empty word.
a(1) = 1 = |{abcdefg}|.
a(2) = 19 = |{abagfedcbcdefg, abagfgfedcbcde, abagfgfededcbc, abcbagfedcdefg, abcbagfgfedcde, abcbagfgfededc, abcbcdedefgagf, abcbcdedefgfga, abcbcdefgagfed, abcdcbagfedefg, abcdcbagfgfede, abcdedcbagfefg, abcdedcbagfgfe, abcdedefgfgabc, abcdefedcbagfg, abcdefgabcdefg, abcdefgagfedcb, abcdefgfedcbag, abcdefgfgabcde}|.
CROSSREFS
Column k=7 of A209349.
Sequence in context: A334565 A183473 A217826 * A368789 A005535 A171226
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Mar 06 2012
STATUS
approved