A392315 - OEIS

%I #9 Feb 17 2026 15:15:39

%S 0,132,3492,63066,1039272,16743744,268318524,4294567158,68718128544,

%T 1099507140156,17592171252756,281474928349650,4503599470329816,

%U 72057593530933368,1152921502978246188,18446744068500898542,295147905162758315088,4722366482816956027380

%N Number of vertex cuts in the n-necklace graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NecklaceGraph.html">Necklace Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCut.html">Vertex Cut</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (24,-150,376,-393,144).

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

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

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

%t Table[16^n - 3^n - 3 (5 3^n - 7) n/2 - 1, {n, 20}]

%t LinearRecurrence[{24, -150, 376, -393, 144}, {0, 132, 3492, 63066, 1039272}, 20]

%t 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]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Feb 17 2026