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A337031 Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2h x 2h x 2h where the walk starts at the center of one of the box's faces. 4
5, 17, 5, 52, 21, 5, 148, 89, 21, 5, 400, 357, 93, 21, 5, 1060, 1424, 405, 93, 21, 5, 2700, 5484, 1789, 409, 93, 21, 5, 6720, 20960, 7705, 1849, 409, 93, 21, 5, 15760, 78412, 33048, 8257, 1853, 409, 93, 21, 5, 36248, 292168, 139032, 37097, 8329, 1853, 409, 93, 21, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..55.

FORMULA

For n <= h, T(h,n) = A116904(n).

Row 1 = T(1,n) = A337033(n).

For n >= (2h+1)^3, T(h,n) = 0 as the walk contains more steps than there are available lattice points in the 2h X 2h X 2h box.

EXAMPLE

T(1,2) = 17. Taking the first step right,left,forward or backward hits the box's edge after which the walks has three directions for the second step, giving 4*3 = 12 walks in all. A first step upward can be followed by a second step in five directions. The total number of 2-step walks is therefore 12+5 = 17.

.

The table begins:

.

5 17 52 148  400 1060  2700   6720  15760   36248    77856   163296    312760...

5 21 89 357 1424 5484 20960  78412 292168 1072272  3919000 14145220  50832492...

5 21 93 405 1789 7705 33048 139032 583256 2422480 10053452 41415564 170419680...

5 21 93 409 1849 8257 37097 164533 728808 3194636 13978148 60739156 263711448...

5 21 93 409 1853 8329 37877 171117 776065 3496769 15758504 70593984 315942684...

5 21 93 409 1853 8333 37961 172165 786089 3577129 16326745 74257917 337994448...

5 21 93 409 1853 8333 37965 172261 787445 3591637 16455441 75254865 344977177...

5 21 93 409 1853 8333 37965 172265 787553 3593341 16475617 75451269 346633713...

5 21 93 409 1853 8333 37965 172265 787557 3593461 16477709 75478437 346921841...

5 21 93 409 1853 8333 37965 172265 787557 3593465 16477841 75480957 346957465...

5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481101 346960453...

5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481105 346960609...

5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481105 346960613...

CROSSREFS

Cf. A116904 (h->infinity), A337033 (h=1), A337023 (start at center of box), A336862 (start at middle of edge), A337035 (start at corner of box), A001412.

Sequence in context: A340706 A093558 A170866 * A125636 A156323 A286816

Adjacent sequences:  A337028 A337029 A337030 * A337032 A337033 A337034

KEYWORD

nonn,walk,tabl

AUTHOR

Scott R. Shannon, Aug 12 2020

STATUS

approved

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Last modified May 8 15:54 EDT 2021. Contains 343666 sequences. (Running on oeis4.)