A238108 a(n) = (n - 1)*(n - 2)*(5*n^4 + 3*n^3 + 34*n^2 - 264*n + 180)/360.

1, 0, 0, 1, 19, 107, 386, 1086, 2597, 5530, 10788, 19647, 33847, 55693, 88166, 135044, 201033, 291908, 414664, 577677, 790875, 1065919, 1416394, 1858010, 2408813, 3089406, 3923180, 4936555, 6159231, 7624449, 9369262

Offset: 0

Author

N. J. A. Sloane, Mar 01 2014

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A059783, A238107.

Programs

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 *)

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