A072852 Number of permutations satisfying i-2<=p(i)<=i+5, i=1..n.

1, 2, 6, 18, 54, 162, 454, 1267, 3613, 10344, 29572, 84436, 240868, 686884, 1959636, 5592181, 15957717, 45533682, 129922090, 370708166, 1057755082, 3018154342, 8611878218, 24572725639, 70114579881, 200061418144, 570845362600

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

Recurrence: a(n) = a(n - 1) + 2*a(n - 2) + 4*a(n - 3) + 7*a(n - 4) + 13*a(n - 5) + 22*a(n - 6) + 28*a(n - 7) - 4*a(n - 8) - 6*a(n - 9) - 6*a(n - 10) - 4*a(n - 12) - 10*a(n - 13) - 10*a(n - 14) + a(n - 16) + a(n - 17) + a(n - 20) + a(n - 21). G.f.: - (x^14 + x^12 + x^10 + x^8 - 6*x^7 - x^6 - 4*x^5 - 3*x^4 - 2*x^3 - x^2 + 1)/(x^21 + x^20 + x^17 + x^16 - 10*x^14 - 10*x^13 - 4*x^12 - 6*x^10 - 6*x^9 - 4*x^8 + 28*x^7 + 22*x^6 + 13*x^5 + 7*x^4 + 4*x^3 + 2*x^2 + x - 1);

Crossrefs

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

Sequence in context: A254941 A182899 A160175 * A072853 A179344 A179349

Adjacent sequences: A072849 A072850 A072851 * A072853 A072854 A072855

Keyword

nonn

Author

Vladimir Baltic, Jul 25 2002

Status

approved