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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.

%I A271610 #13 Feb 16 2025 08:33:33
%S A271610 1,3,2,6,240,2238,2196,37004,20454036,970623228,2317631400,
%T A271610 216893681800,1257138602103744,316487245419538728,2326335506123418128,
%U A271610 1208982377794384163088,63184698521304672890081520,85953148896748583125564477008,2220650888749669503773432361504
%N 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.
%C A271610 In other words, the number of maximum matchings in the (n-1)-triangular grid graph. - _Eric W. Weisstein_, Jun 14 2017
%C A271610 Column 1 of A271617.
%H A271610 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>
%H A271610 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>
%H A271610 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%F A271610 a(n) = A288852(n,floor(n*(n+1)/4)). - _Alois P. Heinz_, Jun 18 2017
%e A271610 All solutions for n=4
%e A271610 .....6........5........6........6........5........5
%e A271610 ....5.1......2.6......5.1......6.1......2.5......2.6
%e A271610 ...2.6.6....5.5.1....2.4.3....5.1.6....5.2.6....4.3.1
%e A271610 Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7
%Y A271610 Cf. A271617, A288852.
%K A271610 nonn
%O A271610 1,2
%A A271610 _R. H. Hardin_, Apr 10 2016
%E A271610 a(16)-a(19) from _Alois P. Heinz_, Jun 15 2017