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A208881
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Number of words either empty or beginning with the first letter of the ternary alphabet, where each letter of the alphabet occurs n times.
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5
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1, 2, 30, 560, 11550, 252252, 5717712, 133024320, 3155170590, 75957810500, 1850332263780, 45508998487680, 1128243920840400, 28159366024288800, 706857555303576000, 17831659928458210560, 451781821468671694110, 11489952898943726476500, 293206575828601020085500
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OFFSET
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0,2
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COMMENTS
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Also the number of (n*k-1)-step walks on k-dimensional cubic lattice from (1,0,...,0) to (n,n,...,n) with positive unit steps in all dimensions.
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LINKS
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FORMULA
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a(n) = (3*n)!/(3 * n!^3) for n>0, a(0) = 1.
n^2*a(n) -3*(3*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Nov 01 2015
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EXAMPLE
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a(0) = 1: the empty word.
a(1) = 2 = |{abc, acb}|.
a(2) = 30 = |{aabbcc, aabcbc, aabccb, aacbbc, aacbcb, aaccbb, ababcc, abacbc, abaccb, abbacc, abbcac, abbcca, abcabc, abcacb, abcbac, abcbca, abccab, abccba, acabbc, acabcb, acacbb, acbabc, acbacb, acbbac, acbbca, acbcab, acbcba, accabb, accbab, accbba}|.
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MAPLE
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a:= n-> `if`(n=0, 1, (3*n)!/(3*n!^3)):
seq(a(n), n=0..20);
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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