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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

%I #12 Jun 18 2017 12:44:07

%S 1,3,2,6,240,2238,2196,37004,20454036,970623228,2317631400,

%T 216893681800,1257138602103744,316487245419538728,2326335506123418128,

%U 1208982377794384163088,63184698521304672890081520,85953148896748583125564477008,2220650888749669503773432361504

%N 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.

%C In other words, the number of maximum matchings in the (n-1)-triangular grid graph. - _Eric W. Weisstein_, Jun 14 2017

%C Column 1 of A271617.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>

%F a(n) = A288852(n,floor(n*(n+1)/4)). - _Alois P. Heinz_, Jun 18 2017

%e All solutions for n=4

%e .....6........5........6........6........5........5

%e ....5.1......2.6......5.1......6.1......2.5......2.6

%e ...2.6.6....5.5.1....2.4.3....5.1.6....5.2.6....4.3.1

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

%Y Cf. A271617, A288852.

%K nonn

%O 1,2

%A _R. H. Hardin_, Apr 10 2016

%E a(16)-a(19) from _Alois P. Heinz_, Jun 15 2017

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)