A289143 -id:A289143 - cp's OEIS frontend

A287230 Number of matchings in the n-triangular honeycomb acute knight graph.

1, 1, 8, 64, 1331, 64000, 6400075, 1404928000, 677298787768, 712186032947200, 1635557819719974912, 8209592592625295700893, 90036881979773511965369428, 2157454308508779392217680572439, 112955975573487831948842897960075264, 12921763288870998051759383983484279183072, 3229803978189426975602886931834056243712000000

Offset: 1

Eric W. Weisstein, May 22 2017

Stan Wagon, Graph Theory Problems from Hexagonal and Traditional Chess, The College Mathematics Journal, Vol. 45, No. 4, September 2014, pp. 278-287.
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching

Cf. A289143, A287204, A289904, A287228, A269869.

a(11) from Eric W. Weisstein, Jun 25 2017
a(12)-a(14) from Andrew Howroyd, Jul 17 2017
a(15)-a(17) from Eric W. Weisstein, Sep 02 2025

A321486 Number of maximal matchings in the n-triangular honeycomb acute knight graph.

Original entry on oeis.org

1, 1, 1, 27, 125, 1728, 76050, 4330747, 485587656, 108023929951, 43807783923008, 32822096942411776, 46378235999539384346, 122583565496980110411000

Offset: 1

Eric W. Weisstein, Nov 11 2018

Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Cf. A287230, A289143.

a(9) from Andrew Howroyd, Nov 11 2018

a(10)-a(14) from Eric W. Weisstein, Jan 26 2024

A348224 Lower matching number of the n-triangular honeycomb acute knight graph.

Original entry on oeis.org

0, 0, 3, 3, 3, 6, 9, 9, 15, 18, 18, 24, 29, 30, 39, 44, 45, 54, 62, 63, 75, 83, 84, 96, 106, 108, 123, 133, 135, 150, 163, 165, 183, 196, 198, 216, 231, 234, 255, 270, 273, 294, 312, 315, 339, 357, 360, 384, 404, 408, 435, 455, 459, 486, 509, 513, 543, 566

Offset: 1

Eric W. Weisstein, Oct 08 2021

Stan Wagon, Graph Theory Problems from Hexagonal and Traditional Chess., The College Mathematics Journal, Vol. 45, No. 4, September 2014, pp. 278-287.
Eric Weisstein's World of Mathematics, Lower Matching Number.
Eric Weisstein's World of Mathematics, Triangular Honeycomb Acute Knight Graph.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,0,0,0,0,0,0,1,-1,0,-1,1).

Cf. A289143 (matching number of the n-triangular honeycomb acute knight graph).

LinearRecurrence[{1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 1}, {0, 0, 3, 3, 3, 6, 9, 9, 15, 18, 18, 24, 29, 30, 39, 44}, 20]
CoefficientList[Series[x^2 (-3 - 3 x^4 - 3 x^6 - 2 x^10 - x^11)/((-1 + x)^3 (1 + x + x^2)^2 (1 + x^3 + x^6 + x^9)), {x, 0, 20}], x]

G.f.: x^3*(-3-3*x^4-3*x^6-2*x^10-x^11)/((-1+x)^3*(1+x+x^2)^2*(1+x^3+x^6+x^9)).

a(n) = a(n-1)+a(n-3)-a(n-4)+a(n-12)-a(n-13)-a(n-15)+a(n-16).

a(16) and beyond from Eric W. Weisstein, Dec 07-08 2024

cp's OEIS Frontend

A287230 Number of matchings in the n-triangular honeycomb acute knight graph.

Views

Author

Keywords

Links

Crossrefs

Extensions

A321486 Number of maximal matchings in the n-triangular honeycomb acute knight graph.

Views

Author

Keywords

Links

Crossrefs

Extensions

A348224 Lower matching number of the n-triangular honeycomb acute knight graph.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions