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A072856 Number of permutations satisfying i-4<=p(i)<=i+4, i=1..n (permutations of length n within distance 4). 87
1, 1, 2, 6, 24, 120, 504, 1902, 6902, 25231, 95401, 365116, 1396948, 5316192, 20135712, 76227216, 288878956, 1095937420, 4159450913, 15783649241, 59878012558, 227128287882, 861543171080, 3268198646496, 12398132725784, 47033439463906, 178423731589482 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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
LINKS
R. H. Hardin, Table of n, a(n) for n = 0..400 (corrected by R. H. Hardin, Jan 19 2019)
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
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.
FORMULA
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
CROSSREFS
Column k=4 of A306209.
Sequence in context: A173845 A258216 A263748 * A228401 A189861 A189570
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Jul 25 2002
EXTENSIONS
a(0)=1 prepended and more terms added by Colin Barker, Jul 06 2013
STATUS
approved

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Last modified February 28 13:26 EST 2024. Contains 370400 sequences. (Running on oeis4.)