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A052178 Number of walks of length n on the simple cubic lattice terminating at height 2 above the (x,y)-plane. 1
1, 12, 99, 700, 4569, 28476, 172508, 1026288, 6033690, 35195512, 204232809, 1181052756, 6814746393, 39267916380, 226097749224, 1301403695520, 7490649175326, 43123589230824, 248351880642630, 1430956006648056, 8249467230853002, 47587180659332248 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..23.

Rigoberto Flórez, Leandro Junes, and José L. Ramírez, Further Results on Paths in an n-Dimensional Cubic Lattice, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.2.

R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6.

MAPLE

b:= proc(n, k) option remember; `if`(min(n, k)<0, 0,

     `if`(max(n, k)=0, 1, b(n-1, k-1)+4*b(n-1, k)+b(n-1, k+1)))

    end:

a:= n-> b(n, 2):

seq(a(n), n=2..25);  # Alois P. Heinz, Oct 28 2021

CROSSREFS

Column 2 of A052179.

Sequence in context: A090230 A133652 A004058 * A322721 A123902 A085374

Adjacent sequences:  A052175 A052176 A052177 * A052179 A052180 A052181

KEYWORD

nonn,walk

AUTHOR

N. J. A. Sloane, Jan 26 2000

EXTENSIONS

More terms and title improved by Sean A. Irvine, Oct 28 2021

STATUS

approved

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Last modified November 27 03:56 EST 2021. Contains 349345 sequences. (Running on oeis4.)