The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216211 Number of self-avoiding walks of any length from NW to SW corners of a grid or lattice with n rows and 4 columns. 5
 1, 4, 28, 178, 1008, 5493, 29879, 163357, 895519, 4911542, 26932856, 147666219, 809584243, 4438588016, 24334993398, 133419407518, 731487440774, 4010463570150, 21987820817522, 120550714106036, 660932932241338, 3623639639745022, 19867014703421770, 108923158026586497, 597183548915194615 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, the ratio of a(n)/a(n-1) appears to converge to around 5.483. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 FORMULA Conjectures from Colin Barker, Nov 18 2017: (Start) G.f.: x*(1 - 8*x + 34*x^2 - 66*x^3 + 21*x^4 + 85*x^5 - 64*x^6 - 45*x^7 + 26*x^8 + 11*x^9 - 3*x^10 - x^11) / ((1 - 8*x + 15*x^2 - 5*x^3 - 9*x^4 + 2*x^5 + x^6)*(1 - 4*x + 7*x^2 - 3*x^3 - 7*x^4 + 2*x^5 + x^6)). a(n) = 12*a(n-1) - 54*a(n-2) + 124*a(n-3) - 133*a(n-4) - 16*a(n-5) + 175*a(n-6) - 94*a(n-7) - 69*a(n-8) + 40*a(n-9) + 12*a(n-10) - 4*a(n-11) - a(n-12) for n>12. (End) EXAMPLE For n=2, using the notation D(own), R(ight), L(eft), U(p), the 4 walks are {D, RDL, RRDLL, RRRDLLL}. MATHEMATICA a[n_] := Block[{t=0, w, b=Array[1&, {n, 4}]}, w[rr_, cc_] := Block[{r, c}, If[rr+cc == 2, t++, Do[{r, c} = {rr, cc} + e; If[0 0, b[[r, c]] = 0; w[r, c]; b[[r, c]] = 1], {e, {{-1, 0}, {1, 0}, {0, 1}, {0, -1}}}]]]; b[[n, 1]] = 0; w[n, 1]; t]; a /@ Range[6] (* Giovanni Resta, Mar 13 2013 *) CROSSREFS Column 4 of A271465. Cf. A005409 for grids with 3 rows, A006189 for grids with 3 columns, and A214931 for grids with 4 rows. Sequence in context: A026298 A181895 A264707 * A366810 A219405 A001396 Adjacent sequences: A216208 A216209 A216210 * A216212 A216213 A216214 KEYWORD nonn,walk AUTHOR Toby Gottfried, Mar 13 2013 EXTENSIONS a(13)-a(14) from Giovanni Resta, Mar 13 2013 Terms a(15) and beyond from Andrew Howroyd, Apr 08 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)