A072855 Number of permutations satisfying i-3<=p(i)<=i+5, i=1..n.

1, 2, 6, 24, 96, 384, 1374, 4718, 16275, 57749, 206756, 739780, 2637348, 9378840, 33318804, 118439044, 421340612, 1499388117, 5335199213, 18980987054, 67522942850, 240204885524, 854523535096, 3040023558788, 10815153542594

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..400

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

Formula

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

Crossrefs

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

Sequence in context: A147939 A147930 A147918 * A179341 A179345 A179350

Adjacent sequences: A072852 A072853 A072854 * A072856 A072857 A072858

Keyword

nonn

Author

Vladimir Baltic, Jul 25 2002

Status

approved