login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A025600 Number of n-move knight paths on 8 X 8 board from given corner to same corner. 2
1, 0, 2, 0, 16, 0, 264, 0, 6828, 0, 218192, 0, 7555444, 0, 269039512, 0, 9671837852, 0, 348829877760, 0, 12595130308612, 0, 454944702478600, 0, 16435098767896556, 0, 593753325451468144, 0, 21450960845508768532, 0, 774978877336933136632, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

From Vaclav Kotesovec, Nov 26 2012: (Start)

G.f.: 1 - 2495/3704 - (-2495 + 257062*x^2 - 10940636*x^4 + 261002480*x^6 - 3944912606*x^8 + 40234628876*x^10 - 286888584304*x^12 + 1458140925208*x^14 - 5325997352347*x^16 + 13961752450926*x^18 - 25982840678332*x^20 + 33572692661080*x^22 - 28997305139008*x^24 + 15706751871616*x^26 - 4743107684352*x^28 + 598878986240*x^30)/(3704*(-1+x)*(1+x)*(-1+2*x)*(1+2*x)*(1 - 3*x - 27*x^2 + 29*x^3 + 162*x^4 - 42*x^5 - 276*x^6 - 16*x^7 + 96*x^8)*(1 + 3*x - 27*x^2 - 29*x^3 + 162*x^4 + 42*x^5 - 276*x^6 + 16*x^7 + 96*x^8)*(1 - 38*x^2 + 546*x^4 - 3712*x^6 + 12253*x^8 - 17754*x^10 + 7408*x^12))

Nonzero terms a(n+2)/a(n) tends to 36.12804064450295915...

(End)

MAPLE

b:= proc(n, i, j) option remember;

      `if`(n<0 or i<0 or i>7 or j<0 or j>7, 0, `if`({n, i, j}={0},

      1, add(b(n-1, i+r[1], j+r[2]), r=[[1, 2], [1, -2], [-1, 2],

      [-1, -2], [2, 1], [2, -1], [-2, 1], [-2, -1]])))

    end:

a:= n-> b(n, 0, 0):

seq(a(n), n=0..40);  # Alois P. Heinz, Jun 28 2012

MATHEMATICA

b[n_, i_, j_] := b[n, i, j] = If[n<0 || i<0 || i>7 || j<0 || j>7, 0, If[Union[{n, i, j}] == {0}, 1, Sum[b[n-1, i+r[[1]], j+r[[2]]], {r, {{1, 2}, {1, -2}, {-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}}}]]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 28 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A086261 A111978 A146558 * A009006 A155585 A236755

Adjacent sequences:  A025597 A025598 A025599 * A025601 A025602 A025603

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)