This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 O. Krafft, M. Schaefer, On the number of permutations within a given distance, Fib. Quart. 40 (5) (2002) 429-434 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 STATUS approved

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 December 18 08:16 EST 2018. Contains 318219 sequences. (Running on oeis4.)