A362501 Number of vertex cuts in the n-alkane graph.

11, 169, 1699, 14989, 125495, 1026273, 8299403, 66752053, 535443679, 4289258377, 34336902707, 274786564317, 2198657885063, 17590724562481, 140731642427611, 1125876523131781, 9007105719897647, 72057219898554585, 576459255745930115, 4611680032197414445

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Alkane Graph.

Eric Weisstein's World of Mathematics, Vertex Cut.

Index entries for linear recurrences with constant coefficients, signature (14,-57,76,-32).

Formula

a(n) = 4*8^n - (49*4^n + 6*n - 13)/9. - Andrew Howroyd, Apr 23 2023

a(n) = 14*a(n-1) - 57*a(n-2) + 76*a(n-3) - 32*a(n-4) for n >= 5. - Pontus von Brömssen, Apr 23 2023

From Elmo R. Oliveira, Apr 27 2026: (Start)

G.f.: x*(11 + 15*x - 40*x^2)/((1 - x)^2*(1 - 4*x)*(1 - 8*x)).

E.g.f.: exp(x)*(13 - 6*x - 49*exp(3*x) + 36*exp(7*x))/9.

a(n) = A013731(n) - A390403(n). (End)

Mathematica

A362501[n_] := 4*8^n - (49*4^n + 6*n - 13)/9; Array[A362501, 20] (* Paolo Xausa, Jan 25 2026 *)
(* Alternative: *)
LinearRecurrence[{14, -57, 76, -32}, {11, 169, 1699, 14989}, 20] (* Paolo Xausa, Jan 25 2026 *)

Crossrefs

Cf. A013731, A390403.

Sequence in context: A255971 A386869 A157944 * A384338 A233290 A167245

Adjacent sequences: A362498 A362499 A362500 * A362502 A362503 A362504

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 23 2023

Extensions

Terms a(8) and beyond from Andrew Howroyd, Apr 23 2023

Status

approved