A391153 - OEIS

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A391153

Array read by antidiagonals: T(n,k) is the number of Hamiltonian rooted triangulations with n internal nodes and k + 3 external nodes, n >= 0, k >= 0.

4

1, 2, 3, 5, 12, 18, 14, 45, 92, 136, 42, 168, 420, 800, 1170, 132, 630, 1842, 4130, 7554, 10962, 429, 2376, 7917, 20162, 42480, 75664, 109158, 1430, 9009, 33616, 95291, 224094, 453350, 792448, 1138032, 4862, 34320, 141570, 440704, 1136814, 2537028, 4986860, 8595120, 12298392

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

See A003122 for programs.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)

P. N. Rathie, The enumeration of Hamiltonian polygons in rooted planar triangulations, Discrete Math., 6 (1973), 163-168.

EXAMPLE

Array begins:

============================================================

n\k | 0 1 2 3 4 ...

----+-------------------------------------------------------

0 | 1 2 5 14 42 ...

1 | 3 12 45 168 630 ...

2 | 18 92 420 1842 7917 ...

3 | 136 800 4130 20162 95291 ...

4 | 1170 7554 42480 224094 1136814 ...

5 | 10962 75664 453350 2537028 13599558 ...

6 | 109158 792448 4986860 29240272 163840054 ...

7 | 1138032 8595120 56251230 342560100 1990716840 ...

8 | 12298392 95895816 648055650 4072483020 24401207684 ...

...

PROG

(PARI) \\ Needs F defined in A003122.

{ my(A=Mat(vector(5, i, Col(F(i+2, 9))))); for(i=1, matsize(A)[1], print(A[i, ])) }

CROSSREFS

Columns k=0..2 are A003122, A003123, A005979.

Rows 0..1 are A000108(k+1), A062561(k+1).

Cf. A146305, A341856.

Sequence in context: A140489 A331101 A193776 * A051915 A064688 A089891

Adjacent sequences: A391150 A391151 A391152 * A391154 A391155 A391156

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Dec 01 2025

STATUS

approved