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A002526 Number of permutations of length n within distance 3 of a fixed permutation.
(Formerly M1671 N0657)
19
1, 1, 2, 6, 24, 78, 230, 675, 2069, 6404, 19708, 60216, 183988, 563172, 1725349, 5284109, 16177694, 49526506, 151635752, 464286962, 1421566698, 4352505527, 13326304313, 40802053896, 124926806216, 382497958000, 1171122069784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For positive n, a(n) equals the permanent of the n X n matrix with 1's along the seven central diagonals, and 0's everywhere else. - John M. Campbell, Jul 09 2011

REFERENCES

V. Baltic, On the number of certain types of strongly restricted permutations, Appl. An. Disc. Math. 4 (2010), 119-135; Doi:10.2298/AADM1000008B; http://pefmath.etf.rs

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. H. Hardin, Table of n, a(n) for n=0..400, Jul 11 2010

Torleiv Kløve, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008. (Table 3, top row)

R. Lagrange, Quelques résultats dans la métrique des permutations, Annales Scientifiques de l'École Normale Supérieure, Paris, 79 (1962), 199-241.

Index entries for linear recurrences with constant coefficients, signature (2,2,0,10,8,-2,-16,-10,-2,4,2,0,2,1).

FORMULA

G.f.: (1-x-2*x^2-2*x^4+x^7+x^8)/(1-2*x-2*x^2-10*x^4-8*x^5+2*x^6+16*x^7+10*x^8+2*x^9-4*x^10-2*x^11-2*x^13-x^14)

a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(4)=24, a(5)=78, a(6)=230, a(7)=675, a(8)=2069, a(9)=6404, a(10)=19708, a(11)=60216, a(12)=183988, a(13)=563172, a(n)=2*a(n-1)+2*a(n-2)+10*a(n-4)+8*a(n-5)- 2*a(n-6)- 16*a(n-7)- 10*a(n-8)-2*a(n-9)+4*a(n-10)+2*a(n-11)+2*a(n-13)+a(n-14). - Harvey P. Dale, Jun 22 2011

MATHEMATICA

CoefficientList[Series[(1-x-2x^2-2x^4+x^7+x^8)/(1-2x-2x^2-10x^4-8x^5+ 2x^6+ 16x^7+10x^8+2x^9-4x^10-2x^11-2x^13-x^14), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 2, 0, 10, 8, -2, -16, -10, -2, 4, 2, 0, 2, 1}, {1, 1, 2, 6, 24, 78, 230, 675, 2069, 6404, 19708, 60216, 183988, 563172}, 51] (* Harvey P. Dale, Jun 22 2011 *)

PROG

(PARI) Vec((1-x-2*x^2-2*x^4+x^7+x^8)/(1-2*x-2*x^2-10*x^4-8*x^5+2*x^6+16*x^7+10*x^8+2*x^9-4*x^10-2*x^11-2*x^13-x^14)+O(x^99)) \\ Charles R Greathouse IV, Jul 16 2011

CROSSREFS

The 14 sequences in Kløve's Table 3 are A002526, A002527, A002529, A188379, A188491, A188492, A188493, A188494, A002528, A188495, A188496, A188497, A188498, A002526.

Cf. A002524.

Sequence in context: A263712 A263698 A263747 * A117665 A068777 A275206

Adjacent sequences:  A002523 A002524 A002525 * A002527 A002528 A002529

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 24 15:07 EDT 2017. Contains 288697 sequences.