The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008305 Triangle read by rows: a(n,k) = number of permutations of [n] allowing i->i+j (mod n), j=0..k-1. 16
 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; text; internal format)
 OFFSET 1,3 COMMENTS The point is, we are counting permutations of [n] = {1,2,...,n} with the restriction that i cannot move by more than k places. Hence the phrase "permutations with restricted displacements". - N. J. A. Sloane, Mar 07 2014 The triangle could have been defined as an infinite square array by setting a(n,k) = n! for k >= n. REFERENCES H. Minc, Permanents, Encyc. Math. #6, 1978, p. 48 LINKS Alois P. Heinz, Rows n = 1..23, flattened Henry Beker and Chris Mitchell, Permutations with restricted displacement, SIAM J. Algebraic Discrete Methods 8 (1987), no. 3, 338--363. MR0897734 (89f:05009) N. S. Mendelsohn, Permutations with confined displacement, Canad. Math. Bull., 4 (1961), 29-38. N. Metropolis, M. L. Stein, P. R. Stein, Permanents of cyclic (0,1) matrices, J. Combin. Theory, 7 (1969), 291-321. Wikipedia, Permanent (mathematics) FORMULA a(n,k) = per(sum(P^j, j=0..k-1)), where P is n X n, P[ i, i+1 (mod n) ]=1, 0's otherwise. a(n,n) - a(n,n-1) = A002467(n). - Alois P. Heinz, Mar 06 2019 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,   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,   ... MAPLE with(LinearAlgebra): a:= (n, k)-> Permanent(Matrix(n,              (i, j)-> `if`(0<=j-i and j-i

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)