A392315 Number of vertex cuts in the n-necklace graph.

0, 132, 3492, 63066, 1039272, 16743744, 268318524, 4294567158, 68718128544, 1099507140156, 17592171252756, 281474928349650, 4503599470329816, 72057593530933368, 1152921502978246188, 18446744068500898542, 295147905162758315088, 4722366482816956027380

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Eric Weisstein's World of Mathematics, Necklace Graph.

Eric Weisstein's World of Mathematics, Vertex Cut.

Index entries for linear recurrences with constant coefficients, signature (24,-150,376,-393,144).

Formula

a(n)=16^n - 3^n - 3*(5*3^n - 7)*n/2 - 1.

a(n) = 24*a(n-1)-150*a(n-2)+376*a(n-3)-393*a(n-4)+144*a(n-5).

G.f.: 6*x^2*(-22-54*x+157*x^2+24*x^3)/((-1+16*x)*(1-4*x+3*x^2)^2).

Mathematica

Table[16^n - 3^n - 3 (5 3^n - 7) n/2 - 1, {n, 20}]
LinearRecurrence[{24, -150, 376, -393, 144}, {0, 132, 3492, 63066, 1039272}, 20]
CoefficientList[Series[6 x (-22 - 54 x + 157 x^2 + 24 x^3)/((-1 + 16 x) (1 - 4 x + 3 x^2)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A023902 A240270 A168180 * A236260 A264179 A228333

Adjacent sequences: A392312 A392313 A392314 * A392316 A392317 A392318

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 17 2026

Status

approved