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A174589 Number of directed Hamiltonian cycles in the Triangle Graph of order n. 1
1, 2, 2, 6, 52, 948, 34428, 2742908, 463849560, 164734305828, 123437602332804, 194965649426622884, 647793073112134906932, 4525859704558897642199864, 66463181964865873238784109324, 2050514181580724375252309339543868 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Triangle Graph of order n has n rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

LINKS

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, Triangular Grid Graph

FORMULA

For n>1, a(n) = 2*A112676(n).

EXAMPLE

For n = 4 the Triangle Graph of order 4 has 10 vertices and 18 edges. If vertices are numbered from left to right in each row and ascending with row numbers, the a(4) = 6 Hamiltonian cycles are (1,2,4,7,8,5,9,10,6,3), (1,2,4,7,8,9,10,6,5,3), (1,2,5,4,7,8,9,10,6,3), (1,3,5,6,10,9,8,7,4,2), (1,3,6,10,9,5,8,7,4,2), (1,3,6,10,9,8,7,4,5,2).

CROSSREFS

Sequence in context: A032117 A137244 A284707 * A326942 A247943 A329571

Adjacent sequences:  A174586 A174587 A174588 * A174590 A174591 A174592

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 29 2010

EXTENSIONS

a(11)-a(16) computed from A112676 by Max Alekseyev, Jul 01 2016

STATUS

approved

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Last modified January 28 03:42 EST 2020. Contains 331317 sequences. (Running on oeis4.)