|
| |
|
|
A079988
|
|
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={0,1,2}.
|
|
0
|
|
|
|
1, 0, 0, 0, 1, 3, 3, 3, 6, 10, 29, 39, 61, 101, 179, 335, 566, 928, 1575, 2705, 4747, 8117, 13782, 23464, 40216, 69209, 118650, 202712, 346508, 593180, 1016874, 1741871, 2981190, 5101520, 8733466, 14956519, 25611753, 43847283, 75061015, 128505176
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
COMMENTS
|
Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,-1,0}.
|
|
|
REFERENCES
|
D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
|
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 4, 4, -1, -3, -2, 1, -4, -3, 1, 4, 0, -1, 1, 1, 0, -1).
|
|
|
FORMULA
|
a(n) = a(n-2) +a(n-3) +a(n-4) +4*a(n-5) +4*a(n-6) -a(n-7) -3*a(n-8) -2*a(n-9) +a(n-10) -4*a(n-11) -3*a(n-12) +a(n-13) +4*a(n-14) -a(n-16) +a(n-17) +a(n-18) -a(n-20) .
G.f.: -(x^14-x^12 -x^11+x^9 -2*x^8+2*x^6 +x^5+x^3 +x^2-1)/( x^20 -x^18 -x^17 +x^16 -4*x^14 -x^13 +3*x^12 +4*x^11 -x^10 +2*x^9 +3*x^8 +x^7 -4*x^6 -4*x^5 -x^4 -x^3 -x^2+1).
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
