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A346793 Triangle T(n,m) read by rows: the number of n X m arrays with nonnegative integers, zeros on the border rows/columns and maximum difference one between any entry and its 4 neighbors. 0
1, 1, 2, 1, 4, 16, 1, 8, 64, 528, 1, 16, 256, 4368, 75536, 1, 32, 1024, 36176, 1312656, 48185392, 1, 64, 4096, 299664, 22844432, 1776652720, 139414770480, 1, 128, 16384, 2482384, 397748880, 65621158928, 10984586881360, 1852311458443344, 1, 256, 65536, 20563984, 6926263568 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The arrays a(i,j) which are counted have constant surrounding borders clamped at a(i,1) = a(i,m) = a(1,j) = a(n,j) =0 , all a(i,j)>=0 and limited slopes |a(i,j)-a(i+1,j)| <= 1, |a(i,j)-a(i-1,j)| <= 1, |a(i,j)-a(i,j+1)| <= 1 and |a(i,j)-a(i,j-1)| <= 1. All rows and columns of the T(n,m) have rational generating functions.
LINKS
R. J. Mathar, Motzkin Islands: a 3-dimensional embeddng of Motzkin paths, vixra:2009.0152 (2020) Table 2.
FORMULA
T(n,m) = T(m,n).
T(n,m) = 2^((m-1)*(n-1)), 1<=m<=3, n>=1.
T(4,m) = 9*T(4,m-1) -4*T(4,m-2) -16*T(4,m-3).
T(5,m) = 21*T(5,m-1) -52*T(5,m-2) -184*T(5,m-3) +32*T(5,m-4) +128*T(5,m-5).
EXAMPLE
The triangle starts) with n>=1, 1<=m<=n as
1
1 2
1 4 16
1 8 64 528
1 16 256 4368 75536
1 32 1024 36176 1312656 48185392
1 64 4096 299664 22844432 1776652720 139414770480
1 128 16384 2482384 397748880 65621158928 10984586881360 ...
1 256 65536 20563984 6926263568 2425367471888 867077331528016 ...
CROSSREFS
Sequence in context: A032174 A212267 A344110 * A087801 A238454 A025228
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Aug 04 2021
STATUS
approved

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Last modified June 16 15:45 EDT 2024. Contains 373432 sequences. (Running on oeis4.)