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
Links
- 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. - _N. J. A. Sloane_, Jan 02 2013
- Index entries for linear recurrences with constant coefficients, signature (1,1,0,2,-2,-1,-1,-1).
Programs
-
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 *)
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) = (1+x)*(1-x+x^2)/((1-x-x^2)*(1+x^2)*(1-x^2-x^4)).