A378790 Lower matching number of the n X n king graph.

0, 2, 3, 6, 8, 14, 17, 24, 28, 38, 43, 54, 60, 74, 81, 96, 104, 122, 131, 150, 160, 182, 193, 216, 228, 254, 267, 294, 308, 338, 353, 384, 400, 434, 451, 486, 504, 542, 561, 600, 620, 662, 683, 726, 748, 794, 817, 864, 888, 938, 963, 1014, 1040, 1094, 1121

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, King Graph.

Eric Weisstein's World of Mathematics, Lower Matching Number.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Formula

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

a(n) = 1*a(n-1)+1*a(n-2)-1*a(n-3)+1*a(n-4)-1*a(n-5)-1*a(n-6)+1*a(n-7).

Mathematica

Table[(3 + (-1)^n + 2 n (-1 + (-1)^n + 3 n) - 4 Cos[n Pi/2] - 4 Sin[n Pi/2])/16, {n, 20}]
LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {0, 2, 3, 6, 8, 14, 17}, 20]
CoefficientList[Series[-((x (2 + x + x^2 + x^3 + x^4))/((-1 + x)^3 (1 + x)^2 (1 + x^2))), {x, 0, 20}], x]

Crossrefs

Sequence in context: A376597 A308909 A369356 * A308958 A326450 A326530

Adjacent sequences: A378786 A378787 A378788 * A378791 A378793 A378796

Keyword

nonn,new

Author

Eric W. Weisstein, Dec 07 2024

Status

approved