A390403 a(n) = (49*4^n + 6*n - 13)/9.

4, 21, 87, 349, 1395, 5577, 22303, 89205, 356811, 1427233, 5708919, 22835661, 91342627, 365370489, 1461481935, 5845927717, 23383710843, 93534843345, 374139373351, 1496557493373, 5986229973459, 23944919893801, 95779679575167, 383118718300629, 1532474873202475

Offset

0,1

Comments

For n >= 1, also the number of mutual-visibility sets in the n-alkane graph.

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Alkane Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

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

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

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

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

a(n) = A013731(n) - A362501(n). (End)

Mathematica

Table[(49 4^n + 6 n - 13)/9, {n, 0, 20}]
(* Alternative: *)
CoefficientList[Series[(-4 + 3 x + 3 x^2)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]
(* Alternative: *)
LinearRecurrence[{6, -9, 4}, {21, 87, 349}, {0, 20}]

Crossrefs

Cf. A013731, A362501.

Sequence in context: A381470 A292126 A174797 * A328345 A371309 A220574

Adjacent sequences: A390400 A390401 A390402 * A390404 A390405 A390406

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 14 2025

Status

approved