A217694 Number of n-variations of the set {1,2,...,n+1} satisfying p(i)-i in {-2,0,2}, i=1..n (an n-variation of the set N_{n+s} = {1,2,...,n+s} is any 1-to-1 mapping p from the set N_n = {1,2,...,n} into N_{n+s} = {1,2,...,n+s}).

1, 1, 2, 4, 8, 12, 21, 35, 60, 96, 160, 260, 429, 693, 1134, 1836, 2992, 4840, 7865, 12727, 20648, 33408, 54144, 87608, 141897, 229593, 371722, 601460, 973560, 1575252, 2549421, 4125051, 6675460, 10801120, 17478176, 28280284, 45761045, 74042925, 119808150

Offset

0,3

Links

Table of n, a(n) for n=0..38.

V. Baltic, Applications of the finite state automata for counting restricted permutations and variations, Yugoslav Journal of Operations Research, 22 (2012), Number 2, 183-198 ; DOI: 10.2298/YJOR120211023B - N. J. A. Sloane, Jan 02 2013

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

Formula

Recurrence: a(n)=a(n-1)+a(n-2)+2*a(n-4)-2*a(n-5)-a(n-6)-a(n-7)-a(n-8).

G.f.: (1+x^3)/(1-x-x^2-2*x^4+2*x^5+x^6+x^7+x^8).

Mathematica

LinearRecurrence[{1, 1, 0, 2, -2, -1, -1, -1}, {1, 1, 2, 4, 8, 12, 21, 35}, 40] (* Harvey P. Dale, Feb 29 2020 *)

Crossrefs

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

Sequence in context: A076651 A368986 A081410 * A027677 A103787 A365076

Adjacent sequences: A217691 A217692 A217693 * A217695 A217696 A217697

Keyword

nonn,easy

Author

Vladimir Baltic, Oct 11 2012

Status

approved