OFFSET
0,8
COMMENTS
Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=3, r=6, I={-2,-1,1,2,3,4,5}.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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, 0, -1, 2, 0, -2, 4, 0, 2, 2, 0, 4, -2, 0, 2, -4, 0, -2, -2, 0, -1, -1, 0, -1).
FORMULA
a(3*k) = (A000930(k))^3.
a(n) = a(n-1) -a(n-3) +2*a(n-4) -2*a(n-6) +4*a(n-7) +2*a(n-9) +2*a(n-10) +4*a(n-12) -2*a(n-13) +2*a(n-15) -4*a(n-16) -2*a(n-18) -2*a(n-19) -a(n-21) -a(n-22) -a(n-24)
G.f.: (1+x^3-x^4-x^5+x^6-2*x^7-x^8-x^9-2*x^10-x^12-x^13-x^15) / ((1-x)*(1+x+x^2)*(1-x-x^3)*(1+3*x^3+7*x^6+9*x^9+7*x^12+3*x^15+x^18))
MATHEMATICA
CoefficientList[Series[(1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18))) \\ G. C. Greubel, Apr 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, May 16 2013
STATUS
approved