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Search: id:A008305
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| A008305 |
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Triangle read by rows: a(n,k) = number of permutations of [ n ] allowing i->i+j (mod n),j=0..k-1. |
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+0
4
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| 1, 1, 2, 1, 2, 6, 1, 2, 9, 24, 1, 2, 13, 44, 120, 1, 2, 20, 80, 265, 720, 1, 2, 31, 144, 579, 1854, 5040, 1, 2, 49, 264, 1265, 4738, 14833, 40320, 1, 2, 78, 484, 2783, 12072, 43387, 133496, 362880, 1, 2, 125, 888, 6208, 30818, 126565, 439792, 1334961, 3628800, 1, 2
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. S. Mendelsohn, Permutations with restricted displacement, Canad. Math. Bull., 4 (1961), 29-38.
H. Minc, Permanents, Encyc. Math. #6, 1978, p. 48
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FORMULA
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a(n, k)=per(sum(P^j, j=0..k-1)), where P is n by n, P[ i, i+1 (mod n) ]=1, 0's otherwise.
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EXAMPLE
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1; 1,2; 1,2,6; 1,2,9,24; etc. (so a(4,3)=9)
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CROSSREFS
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A000142, A000166, A000179, A000183, A004307, A000211, A000496, A000803, A004306.
Cf. A000804, A000805.
Sequence in context: A096179 A166350 A133643 this_sequence A133644 A152431 A143965
Adjacent sequences: A008302 A008303 A008304 this_sequence A008306 A008307 A008308
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KEYWORD
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tabl,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Comments and more terms from Len Smiley (smiley(AT)math.uaa.alaska.edu)
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 02 2003
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