A005507 - OEIS

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A005507

Number of unrooted triangulations with reflection symmetry of a hexagon with n internal nodes.
(Formerly M1622)

2, 6, 18, 52, 166, 524, 1722, 5664, 19072, 64408, 220676, 758864, 2634734, 9180872, 32208376, 113371636, 401067522, 1423073892, 5068961452, 18103192360, 64853607912, 232872927444, 838311889890, 3023961593292, 10931277735230, 39586258360246, 143617299291242

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

OFFSET

0,1

COMMENTS

These are also called [n,3]-triangulations.

REFERENCES

C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)

C. F. Earl & N. J. A. Sloane, Correspondence, 1980-1981

FORMULA

a(n) = 2 * A005502(n) - A005495(n) (based on Max Alekseyev's formula, cf. A005500 and A005501).

CROSSREFS

Column k=3 of the array in A169809.

Cf. A005495, A005502.

Sequence in context: A077835 A077984 A052979 * A252822 A094864 A120010

Adjacent sequences: A005504 A005505 A005506 * A005508 A005509 A005510

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(5)-a(10) from Altug Alkan and Manfred Scheucher, Mar 08 2018

Name clarified and terms a(11) and beyond from Andrew Howroyd, Feb 21 2021

STATUS

approved