%I #19 Jul 29 2024 09:51:00
%S 1,2,6,24,96,384,1374,4718,16275,57749,206756,739780,2637348,9378840,
%T 33318804,118439044,421340612,1499388117,5335199213,18980987054,
%U 67522942850,240204885524,854523535096,3040023558788,10815153542594
%N Number of permutations satisfying i-3<=p(i)<=i+5, i=1..n.
%H R. H. Hardin, <a href="/A072855/b072855.txt">Table of n, a(n) for n = 1..400</a>
%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 <a href="/index/Rec#order_56">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, 8, 20, 46, 114, 242, 354, -250, -490, -660, -496, -24, -1242, -2430, -2270, -566, 2241, 5071, 4259, -632, 1392, 6396, 5596, -132, 1316, -6220, -11116, 736, 344, -5128, -3684, 1148, -388, 980, 1665, 239, -199, 688, 540, -106, 50, -78, -102, -58, 22, -44, -40, 0, -2, 2, 2, 2, -1, 1, 1).
%F G.f.: -(1- 2*x^2 - 7*x^3 - 16*x^4 - 28*x^5 - 32*x^6 - 58*x^7 - 156*x^8 + 67*x^9 + 76*x^10 + 68*x^11 + 145*x^12 + 12*x^13 + 156*x^14 + 180*x^15 + 704*x^16 + 344*x^17 - 454*x^18 - 276*x^19 - 480*x^20 + 158*x^21 - 260*x^22 - 116*x^23 - 780*x^24 - 756*x^25 + 168*x^26 + 206*x^27 + 900*x^28 - 340*x^29 + 126*x^30 + 132*x^31 + 276*x^32 + 28*x^33 + 16*x^34 + 24*x^35 - 107*x^36 + 36*x^37 - 14*x^38 - 7*x^39 - 28*x^40 - 4*x^42 - 2*x^43 + 4*x^44 - x^45 + x^48) / (-1 + x + 3*x^2 + 8*x^3 + 20*x^4 + 46*x^5 + 114*x^6 + 242*x^7 + 354*x^8 - 250*x^9 - 490*x^10 - 660*x^11 - 496*x^12 - 24*x^13 - 1242*x^14 - 2430*x^15 - 2270*x^16 - 566*x^17 + 2241*x^18 + 5071*x^19 + 4259*x^20 - 632*x^21 + 1392*x^22 + 6396*x^23 + 5596*x^24 - 132*x^25 + 1316*x^26 - 6220*x^27 - 11116*x^28 + 736*x^29 + 344*x^30 - 5128*x^31 - 3684*x^32 + 1148*x^33 - 388*x^34 + 980*x^35 + 1665*x^36 + 239*x^37 - 199*x^38 + 688*x^39 + 540*x^40 - 106*x^41 + 50*x^42 - 78*x^43 - 102*x^44 - 58*x^45 + 22*x^46 - 44*x^47 - 40*x^48 - 2*x^50 + 2*x^51 + 2*x^52 + 2*x^53 - x^54 + x^55 + x^56). - _Vaclav Kotesovec_, Dec 01 2012
%Y Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K nonn
%O 1,2
%A _Vladimir Baltic_, Jul 25 2002