cp's OEIS Frontend

A189600 Number of permutations of 1..n with displacements restricted to {-7,-6,-5,-4,-3,-2,0,1}.

%I A189600 #27 Mar 25 2020 10:54:26
%S A189600 1,1,2,4,7,12,21,37,64,111,194,339,591,1030,1796,3132,5461,9522,16604,
%T A189600 28953,50485,88030,153498,267655,466710,813802,1419027,2474358,
%U A189600 4314538,7523260,13118310,22874400,39886095,69549390,121273283,211464244
%N A189600 Number of permutations of 1..n with displacements restricted to {-7,-6,-5,-4,-3,-2,0,1}.
%C A189600 a(n+1) is the number of multus bitstrings of length n with no runs of 8 ones. - _Steven Finch_, Mar 25 2020
%H A189600 R. H. Hardin, <a href="/A189600/b189600.txt">Table of n, a(n) for n = 1..200</a>
%H A189600 Steven Finch, <a href="https://arxiv.org/abs/2003.09458">Cantor-solus and Cantor-multus distributions</a>, arXiv:2003.09458 [math.CO], 2020.
%H A189600 Robert Israel, <a href="/A189600/a189600_1.pdf">Proof of empirical recurrence</a>
%F A189600 Empirical: a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8).
%F A189600 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
%F A189600 Empirical recurrence verified (see link). - _Robert Israel_, Jan 27 2019
%e A189600 Some solutions for n=13:
%e A189600    1  1  1  4  1  5  1  6  1  1  1  5  3  3  5  1
%e A189600    8  2  2  1  2  1  2  1  2  2  4  1  1  1  1  4
%e A189600    2  3  3  2  3  2  3  2 10  3  2  2  2  2  2  2
%e A189600    3  4  4  3  7  3  4  3  3  4  3  3  4  8  3  3
%e A189600    4  5  7  9  4  4  7  4  4 12  5  4  5  4  4  5
%e A189600    5  8  5  5  5  6  5  5  5  5  6  6 11  5  9 10
%e A189600    6  6  6  6  6  9  6  7  6  6  7 12  6  6  6  6
%e A189600    7  7 12  7  8  7  8  8  7  7  8  7  7  7  7  7
%e A189600   13 13  8  8  9  8 13  9  8  8  9  8  8 13  8  8
%e A189600    9  9  9 10 12 10  9 10  9  9 10  9  9  9 10  9
%e A189600   10 10 10 11 10 13 10 11 11 10 13 10 10 10 13 11
%e A189600   11 11 11 12 11 11 11 12 12 11 11 11 12 11 11 12
%e A189600   12 12 13 13 13 12 12 13 13 13 12 13 13 12 12 13
%p A189600 f:= proc(n) option remember; local k;
%p A189600   if n < 0 then return 0 fi;
%p A189600   f(n-1) + add(f(n-k),k=3..8)
%p A189600 end proc:
%p A189600 f(0):= 1:
%p A189600 map(f, [$1..60]); # _Robert Israel_, Jan 27 2019
%K A189600 nonn
%O A189600 1,3
%A A189600 _R. H. Hardin_, Apr 24 2011