A378788 Lower matching number of the (n,n)-stacked book graph.

1, 2, 4, 6, 10, 14, 17, 24, 30, 34, 44, 52, 57, 70, 80, 86, 102, 114, 121, 140, 154, 162, 184, 200, 209, 234, 252, 262, 290, 310, 321, 352, 374, 386, 420, 444, 457, 494, 520, 534, 574, 602, 617, 660, 690, 706, 752, 784, 801, 850, 884, 902, 954, 990, 1009

Offset

1,2

Links

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

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

Eric Weisstein's World of Mathematics, Stacked Book Graph.

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Formula

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

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

Mathematica

Table[1/27 (6 + 6 n + 9 n^2 + 6 (n + 2) ChebyshevU[n, -1/2] + 3 (1 + n) ChebyshevU[n + 1, -1/2] - 15 Cos[2 n Pi/3] + 11 Sqrt[3] Sin[2 n Pi/3]), {n, 20}]
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 2, 4, 6, 10, 14, 17}, 20]
CoefficientList[Series[-(1 + x + 2 x^2 + 2 x^4)/((-1 + x)^3 (1 + x + x^2)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A109807 A259645 A191113 * A345211 A125964 A288526

Adjacent sequences: A378785 A378786 A378787 * A378789 A378790 A378791

Keyword

nonn

Author

Eric W. Weisstein, Dec 07 2024

Status

approved