A390403 - OEIS

%I #39 May 02 2026 15:42:24

%S 4,21,87,349,1395,5577,22303,89205,356811,1427233,5708919,22835661,

%T 91342627,365370489,1461481935,5845927717,23383710843,93534843345,

%U 374139373351,1496557493373,5986229973459,23944919893801,95779679575167,383118718300629,1532474873202475

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

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

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).

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

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

%F From _Elmo R. Oliveira_, Apr 27 2026: (Start)

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

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

%t Table[(49 4^n + 6 n - 13)/9, {n, 0, 20}]

%t (* Alternative: *)

%t CoefficientList[Series[(-4 + 3 x + 3 x^2)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]

%t (* Alternative: *)

%t LinearRecurrence[{6, -9, 4}, {21, 87, 349}, {0, 20}]

%Y Cf. A013731, A362501.

%K nonn,easy

%O 0,1

%A _Eric W. Weisstein_, Dec 14 2025