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A002526
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Number of permutations of length n within distance 3 of a fixed permutation.
(Formerly M1671 N0657)
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20
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| For positive n, a(n) equals the permanent of the nXn matrix with 1's along the seven central diagonals, and 0's everywhere else. [From John M. Campbell, Jul 09 2011]
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REFERENCES
| R. Lagrange, Quelques re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.
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).
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LINKS
| R. H. Hardin, Table of n, a(n) for n=0..400, Jul 11 2010
Torleiv Klove, 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 re'sultats dans la me'trique des permutations, Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure, Paris, 79 (1962), 199-241.
Index to sequences with linear recurrences with constant coefficients, signature (2,2,0,10,8,-2,-16,-10,-2,4,2,0,2,1).
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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) [From Harvey P. Dale, June 22 2011]
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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] (* From Harvey P. Dale, June 22 2011 *)
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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
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CROSSREFS
| The 14 sequences in Klove's Table 3 are A002526, A002527, A002529, A188379, A188491, A188492, A188493, A188494, A002528, A188495, A188496, A188497, A188498, A002526.
Cf. A002524.
Sequence in context: A147938 A147929 A147921 * A117665 A068777 A095110
Adjacent sequences: A002523 A002524 A002525 * A002527 A002528 A002529
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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