A189600 Number of permutations of 1..n with displacements restricted to {-7,-6,-5,-4,-3,-2,0,1}.
1, 1, 2, 4, 7, 12, 21, 37, 64, 111, 194, 339, 591, 1030, 1796, 3132, 5461, 9522, 16604, 28953, 50485, 88030, 153498, 267655, 466710, 813802, 1419027, 2474358, 4314538, 7523260, 13118310, 22874400, 39886095, 69549390, 121273283, 211464244
Offset: 1
Keywords
Examples
Some solutions for n=13: 1 1 1 4 1 5 1 6 1 1 1 5 3 3 5 1 8 2 2 1 2 1 2 1 2 2 4 1 1 1 1 4 2 3 3 2 3 2 3 2 10 3 2 2 2 2 2 2 3 4 4 3 7 3 4 3 3 4 3 3 4 8 3 3 4 5 7 9 4 4 7 4 4 12 5 4 5 4 4 5 5 8 5 5 5 6 5 5 5 5 6 6 11 5 9 10 6 6 6 6 6 9 6 7 6 6 7 12 6 6 6 6 7 7 12 7 8 7 8 8 7 7 8 7 7 7 7 7 13 13 8 8 9 8 13 9 8 8 9 8 8 13 8 8 9 9 9 10 12 10 9 10 9 9 10 9 9 9 10 9 10 10 10 11 10 13 10 11 11 10 13 10 10 10 13 11 11 11 11 12 11 11 11 12 12 11 11 11 12 11 11 12 12 12 13 13 13 12 12 13 13 13 12 13 13 12 12 13
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
- Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.
- Robert Israel, Proof of empirical recurrence
Programs
-
Maple
f:= proc(n) option remember; local k; if n < 0 then return 0 fi; f(n-1) + add(f(n-k),k=3..8) end proc: f(0):= 1: map(f, [$1..60]); # Robert Israel, Jan 27 2019
Formula
Empirical: a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8).
Empirical g.f.: -x*(1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) / ( (x^2 + 1)*(x^6 + x^5 + x^2 + x - 1) ). - R. J. Mathar, Jul 25 2012
Empirical recurrence verified (see link). - Robert Israel, Jan 27 2019
Comments