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%I #39 Jan 29 2019 10:35:39
%S 1,1,2,6,24,120,504,1902,6902,25231,95401,365116,1396948,5316192,
%T 20135712,76227216,288878956,1095937420,4159450913,15783649241,
%U 59878012558,227128287882,861543171080,3268198646496,12398132725784,47033439463906,178423731589482
%N Number of permutations satisfying i-4<=p(i)<=i+4, i=1..n (permutations of length n within distance 4).
%C a(n) equals the permanent of the n X n matrix with 1's along the nine central diagonals and 0's everywhere else. - _John M. Campbell_, Jul 09 2011
%H R. H. Hardin, <a href="/A072856/b072856.txt">Table of n, a(n) for n = 0..400</a> (corrected by _R. H. Hardin_, Jan 19 2019)
%H Vladimir Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
%H Torleiv Kløve, <a href="http://www.ii.uib.no/publikasjoner/texrap/pdf/2008-376.pdf"> Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. </a> Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
%F G.f.: (1 -2*x -3*x^2 -x^3 +4*x^4 -31*x^5 -5*x^6 +32*x^7 -21*x^8 +129*x^9 +94*x^10 -83*x^11 +11*x^12 -192*x^13 -59*x^14 +63*x^15 -16*x^16 +3*x^17 -29*x^18 -46*x^19 -57*x^20 +253*x^21 -28*x^22 -101*x^23 +17*x^24 +104*x^25 -15*x^26 -29*x^27 +10*x^28 -x^29 +x^30 -x^32 -3*x^33 +x^35) / (1 -3*x -2*x^2 +x^3 +x^4 -70*x^5 -39*x^6 +31*x^7 +114*x^8 +522*x^9 +184*x^10 -34*x^11 -46*x^12 -1444*x^13 -202*x^14 +606*x^15 -1204*x^16 -198*x^17 +804*x^18 -542*x^19 +26*x^20 +2372*x^21 +318*x^22 -1582*x^23 +328*x^24 +2018*x^25 +222*x^26 -810*x^27 -184*x^28 +706*x^29 +14*x^30 -204*x^31 -70*x^32 -14*x^33 -28*x^34 +22*x^35 +11*x^36 -47*x^37 +8*x^38 +11*x^39 +x^40 +4*x^41 -x^42 -x^43). - _Torleiv Kløve_, Jan 13 2009; corrected by _Colin Barker_, Jul 06 2013
%Y Cf. A002524..A002529, A072827, A072850..A072856, A079955..A080014.
%Y Column k=4 of A306209.
%K nonn
%O 0,3
%A _Vladimir Baltic_, Jul 25 2002
%E a(0)=1 prepended and more terms added by _Colin Barker_, Jul 06 2013
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