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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. 8
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

Table of n, a(n) for n=0..55.

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)).

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

CROSSREFS

Rows and columns include A002709, A002710, A002711, A001683, A210696, A005498, A005499.

Sequence in context: A074720 A323456 A326058 * A058359 A261608 A110332

Adjacent sequences:  A262583 A262584 A262585 * A262587 A262588 A262589

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 20 2015

STATUS

approved

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Last modified September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)