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A072827 Number of permutations satisfying i-2<=p(i)<=i+3, i=1..n. 77
1, 2, 6, 18, 46, 115, 301, 792, 2068, 5380, 14020, 36581, 95413, 248786, 648714, 1691686, 4411530, 11503991, 29998953, 78228640, 203998184, 531969064, 1387222648, 3617479225, 9433351129, 24599481138, 64148406350, 167280683834 (list; graph; refs; listen; history; text; internal format)
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

Index entries for linear recurrences with constant coefficients, signature (1,2,3,5,6,-1,-1,0,-1,-1).

FORMULA

Recurrence: a(n) = a(n-1)+2*a(n-2)+3*a(n-3)+5*a(n-4)+6*a(n-5)-a(n-6) -a(n-7)-a(n-9)-a(n-10).

G.f.: (x^5+x^3+x^2-1)/(x^10+x^9+x^7+x^6-6*x^5-5*x^4-3*x^3-2*x^2-x+1).

MATHEMATICA

LinearRecurrence[{1, 2, 3, 5, 6, -1, -1, 0, -1, -1}, {1, 2, 6, 18, 46, 115, 301, 792, 2068, 5380}, 30] (* Harvey P. Dale, Aug 15 2014 *)

PROG

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; -1, -1, 0, -1, -1, 6, 5, 3, 2, 1]^(n-1)*[1; 2; 6; 18; 46; 115; 301; 792; 2068; 5380])[1, 1] \\ Charles R Greathouse IV, Jul 28 2015

CROSSREFS

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

Sequence in context: A054136 A232600 A140960 * A248169 A002529 A217526

Adjacent sequences:  A072824 A072825 A072826 * A072828 A072829 A072830

KEYWORD

nonn,easy

AUTHOR

Vladimir Baltic, Jul 21 2002

STATUS

approved

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.