A348224 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..58.

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).

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).

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]

CROSSREFS

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

Sequence in context: A214361 A124449 A262877 * A141094 A132972 A113920