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

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

Author

Eric W. Weisstein, Oct 08 2021

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

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

Programs

Mathematica

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]

Formula

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).

Extensions

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