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A110106
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a(n) is the number of coverings of 1...n by cyclic words of length 3n, such that each value from 1 to n appears precisely twice. That is, the union of all the letters in all of the words of a given covering is the multiset {1,1,2,2,...,n,n}. Repeats of words are allowed in a given covering.
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3
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OFFSET
| 0,2
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COMMENTS
| P-recursive
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FORMULA
| diff eq satisfied by F(t)=sum a(n) t^(3n)/(3n!) {F(0) = 1, (6*t^2-12*t^5+t^8)*F(t)+(-4*t^6-2+16*t^3)*diff(F(t), t)+4*t^4*diff(diff(F(t), t), t)} recurrence satisfied by a(n): {(40320+328752*n+78732*n^7+6561*n^8+1816668*n^3+1818369*n^4+1102248*n^5+398034*n^6+1063116*n^2)*a(n)+(-161280-508608*n-453600*n^3-173340*n^4-34992*n^5-2916*n^6-661104*n^2)*a(n+1)+(12432+20070*n+12114*n^2+3240*n^3+324*n^4)*a(n+2)-2*a(n+3), a(1) = 6, a(0) = 1, a(2) = 3960}
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EXAMPLE
| a(1)=6: {123, 132} {112, 233} {113, 322} {133, 122} {123, 123} {132, 132}
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CROSSREFS
| Cf. A052205, A110104, A110105, A108242.
Sequence in context: A048542 A140173 A158663 * A024087 A161845 A099723
Adjacent sequences: A110103 A110104 A110105 * A110107 A110108 A110109
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KEYWORD
| easy,nonn
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AUTHOR
| Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
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