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A262586 Square array T(n,m) (n>=0, m>=0) read by antidiagonals downwards giving number of rooted triangulations of type [n,m] up to orientation-preserving isomorphisms. 13
1, 1, 1, 1, 2, 1, 4, 5, 6, 5, 6, 16, 21, 26, 24, 19, 48, 88, 119, 147, 133, 49, 164, 330, 538, 735, 892, 846, 150, 559, 1302, 2310, 3568, 4830, 5876, 5661, 442, 1952, 5005, 9882, 16500, 24596, 33253, 40490, 39556, 1424, 6872, 19504, 41715, 75387, 120582, 176354, 237336, 290020, 286000, 4522 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
W. G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768. [Annotated scanned copy]. See Table 1 (with a typo at G(n=1,m=6)).
Jean-François Alcover, Mathematica code
FORMULA
Brown (Eq. 6.3) gives a formula.
EXAMPLE
The first few rows are:
1, 1, 1, 4, 6, 19, 49, 150, 442, 1424, 4522, 14924, 49536, ...
1, 2, 5, 16, 48, 164, 559, 1952, ...
1, 6, 21, 88, 330, 1302, 5005, 19504, 75582, 294140, ...
5, 26, 119, 538, 2310, 9882, 41715, 175088, 730626, ...
...
The first few antidiagonals are:
1,
1,1,
1,2,1,
4,5,6,5,
6,16,21,26,24,
19,48,88,119,147,133,
49,164,330,538,735,892,846,
...
MAPLE
A262586 := proc(n, m)
BrownG(n, m) ; # procedure in A210696
end proc:
for d from 0 to 12 do
for n from 0 to d do
printf("%d, ", A262586(n, d-n)) ;
end do:
end do: # R. J. Mathar, Oct 21 2015
MATHEMATICA
See LINKS section.
CROSSREFS
Rows and columns include A002709, A002710, A002711, A001683, A210696, A005498, A005499.
Sequence in context: A074720 A323456 A326058 * A058359 A261608 A351250
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Oct 20 2015
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)