|
| |
|
|
A151254
|
|
Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1)}
|
|
6
| |
|
|
1, 4, 20, 96, 480, 2368, 11840, 58880, 294400, 1468416, 7342080, 36667392, 183336960, 916144128, 4580720640, 22896574464, 114482872320, 572320645120, 2861603225600, 14306741583872, 71533707919360, 357650927714304, 1788254638571520, 8941026626502656, 44705133132513280, 223522175800311808
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Hankel transform is 4^C(n+1,2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 01 2009]
|
|
|
LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
|
|
|
FORMULA
| a(n)=sum{k=0..n, A120730(n,k)*4^k}. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 01 2009]
a(2n+2)=5*a(2n+1), a(2n+1)=5*a(2n)-4^n*A000108(n)=5*a(2n)-A151403(n). G.f.: (sqrt(1-16*x^2)+8x-1)/(8x*(1-5x)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 02 2009]
|
|
|
MATHEMATICA
| aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
|
|
|
CROSSREFS
| Sequence in context: A099025 A008353 A057087 * A098225 A073532 A178874
Adjacent sequences: A151251 A151252 A151253 * A151255 A151256 A151257
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
