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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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10
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The triangle could have been defined as an array: a(n,k) = n! for k>=n.
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REFERENCES
| 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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LINKS
| Alois P. Heinz, Rows n = 1..20, flattened
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FORMULA
| 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
| a(4,3) = 9 because 9 permutations of {1,2,3,4} are allowed if each i can be placed on 3 positions i+0, i+1, i+2 (mod 4): 1234, 1423, 1432, 3124, 3214, 3412, 4123, 4132, 4213.
Triangle begins:
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;
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MAPLE
| with (LinearAlgebra):
a:= (n, k)-> Permanent (Matrix (n,
(i, j)-> `if` (0<=j-i and j-i<k or j-i<k-n, 1, 0))):
seq (seq (a (n, k), k=1..n), n=1..10);
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CROSSREFS
| Cf. A000142, A000166, A000179, A000183, A004307, A000211, A000496, A000803, A004306.
Cf. A000804, A000805.
Sequence in context: A096179 A166350 A133643 * A133644 A152431 A143965
Adjacent sequences: A008302 A008303 A008304 * A008306 A008307 A008308
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KEYWORD
| tabl,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| 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
Edited by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 18 2010
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