A072856 Number of permutations satisfying i-4<=p(i)<=i+4, i=1..n (permutations of length n within distance 4).
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
Offset: 0
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.
- Index entries for linear recurrences with constant coefficients, signature (3, 2, -1, -1, 70, 39, -31, -114, -522, -184, 34, 46, 1444, 202, -606, 1204, 198, -804, 542, -26, -2372, -318, 1582, -328, -2018, -222, 810, 184, -706, -14, 204, 70, 14, 28, -22, -11, 47, -8, -11, -1, -4, 1, 1).
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
Extensions
a(0)=1 prepended and more terms added by Colin Barker, Jul 06 2013
Comments