OFFSET
0,5
COMMENTS
n!*a(n) = number of self-avoiding paths in n-cube from 00...0 to 11...1 with two back-steps.
LINKS
J. Berestycki, É. Brunet, Z. Shi, Accessibility percolation with backsteps, arXiv preprint arXiv:1401.6894, 2014
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=19, a(5)=107, a(6)=386, a(n)= 7*a(n-1)- 21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Mar 15 2015
G.f.: ( -1+34*x^3-47*x^4+26*x^5-8*x^6+7*x-21*x^2 ) / (x-1)^7 . - R. J. Mathar, Apr 23 2015
MATHEMATICA
Table[(n-1)(n-2)(5n^4+3n^3+34n^2-264n+180)/360, {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 0, 0, 1, 19, 107, 386}, 40] (* Harvey P. Dale, Mar 15 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 01 2014
STATUS
approved