A387581 Number of matchings in the n-trapezohedral graph.

2, 6, 27, 108, 399, 1398, 4714, 15438, 49407, 155196, 480027, 1465566, 4425122, 13233678, 39246459, 115536348, 337905279, 982497918, 2841742762, 8180378886, 23446955727, 66940332876, 190423667067, 539897845398, 1526058571394, 4301289034998, 12091553244219

Offset

0,1

Comments

Sequence extended to a(0) using the formula/recurrence.

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Independent Edge Set.

Eric Weisstein's World of Mathematics, Trapezohedral Graph.

Index entries for linear recurrences with constant coefficients, signature (9,-30,45,-30,9,-1).

Formula

a(n) = 9*a(n-1)-30*a(n-2)+45*a(n-3)-30*a(n-4)+9*a(n-5)-a(n-6).

G.f.: -(-2+12*x-33*x^2+45*x^3-27*x^4+6*x^5)/(1-3*x+x^2)^3.

E.g.f.: exp(3*x/2)*(5*(10 + 15*x + 7*x^2)*cosh(sqrt(5)*x/2) + sqrt(5)*x*(41 + 15*x)*sinh(sqrt(5)*x/2))/25. - Stefano Spezia, Sep 02 2025

Mathematica

Table[((n^2 + 5) LucasL[2 n] + 12 n Fibonacci[2 n])/5, {n, 0, 20}]
LinearRecurrence[{9, -30, 45, -30, 9, -1}, {6, 27, 108, 399, 1398, 4714}, {0, 20}]
CoefficientList[Series[-(-2 + 12 x - 33 x^2 + 45 x^3 - 27 x^4 + 6 x^5)/(1 - 3 x + x^2)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A027213 A027237 A027245 * A344495 A391295 A193385

Adjacent sequences: A387578 A387579 A387580 * A387582 A387583 A387584

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 02 2025

Status

approved