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.
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
Offset: 0
Examples
Array begins: ============================================================== n\k | 0 1 2 3 4 5 6 ... ----+--------------------------------------------------------- 0 | 1 1 1 4 6 19 49 ... 1 | 1 2 5 16 48 164 559 ... 2 | 1 6 21 88 330 1302 5005 ... 3 | 5 26 119 538 2310 9882 41715 ... 4 | 24 147 735 3568 16500 75387 338685 ... 5 | 133 892 4830 24596 120582 578622 2730728 ... 6 | 846 5876 33253 176354 900240 4493168 22037055 ... 7 | 5661 40490 237336 1298732 6849810 35286534 178606610 ... ... 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, ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
- Jean-François Alcover, Mathematica code
- 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)).
- L. March and C. F. Earl, On Counting Architectural Plans, Environment and Planning B, 4 (1977), 57-80. See Table 2.
Crossrefs
Programs
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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
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Mathematica
(* See LINKS section. *)
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PARI
\\ See Links in A169808 for PARI program file. { for(n=0, 7, for(k=0, 7, print1(OrientedTriangs(n,k), ", ")); print) } \\ Andrew Howroyd, Nov 23 2024
Formula
Brown (Eq. 6.3) gives a formula.