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Search: id:A079990
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| A079990 |
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Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-1,2}. |
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+0
1
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| 1, 1, 1, 2, 6, 16, 36, 73, 157, 353, 797, 1776, 3916, 8636, 19145, 42504, 94286, 208948, 462907, 1025863, 2274069, 5040891, 11173063, 24763854, 54886846, 121655063, 269646786, 597664017, 1324697483, 2936135519, 6507831521, 14424377636
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OFFSET
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0,4
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COMMENT
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Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,1}.
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REFERENCES
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D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
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FORMULA
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Recurrence: a(n) = a(n-1)+a(n-2)+2*a(n-3)+a(n-4)+4*a(n-5)+7*a(n-6)-4*a(n-7)-a(n-8)+a(n-9)+7*a(n-10)+3*a(n-11)-7*a(n-12)+2*a(n-13)+3*a(n-14)-3*a(n-16)-2*a(n-17)+a(n-18)-a(n-19)-a(n-20) G.f.: -(x^14-x^12+2*x^11-x^9+2*x^6-x^5+2*x^3+x^2-1)/(x^20+x^19-x^18+2*x^17+3*x^16-3*x^14-2*x^13+7*x^12-3*x^11-7*x^10-x^9+x^8+4*x^7-7*x^6-4*x^5-x^4-2*x^3-x^2-x+1)
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Adjacent sequences: A079987 A079988 A079989 this_sequence A079991 A079992 A079993
Sequence in context: A140131 A005676 A038503 this_sequence A127902 A053210 A066641
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic (baltic(AT)galeb.etf.bg.ac.yu), Feb 17 2003
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