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A271610 Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than 1 elements linked to themselves. 1
1, 3, 2, 6, 240, 2238, 2196, 37004, 20454036, 970623228, 2317631400, 216893681800, 1257138602103744, 316487245419538728, 2326335506123418128, 1208982377794384163088, 63184698521304672890081520, 85953148896748583125564477008, 2220650888749669503773432361504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In other words, the number of maximum matchings in the (n-1)-triangular grid graph. - Eric W. Weisstein, Jun 14 2017

Column 1 of A271617.

LINKS

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Maximum Independent Edge Set

Eric Weisstein's World of Mathematics, Triangular Grid Graph

FORMULA

a(n) = A288852(n,floor(n*(n+1)/4)). - Alois P. Heinz, Jun 18 2017

EXAMPLE

All solutions for n=4

.....6........5........6........6........5........5

....5.1......2.6......5.1......6.1......2.5......2.6

...2.6.6....5.5.1....2.4.3....5.1.6....5.2.6....4.3.1

Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7

CROSSREFS

Cf. A271617, A288852.

Sequence in context: A086550 A266239 A018864 * A019951 A019971 A330501

Adjacent sequences:  A271607 A271608 A271609 * A271611 A271612 A271613

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 10 2016

EXTENSIONS

a(16)-a(19) from Alois P. Heinz, Jun 15 2017

STATUS

approved

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Last modified June 25 10:28 EDT 2021. Contains 345453 sequences. (Running on oeis4.)