A394342 - OEIS

%I #22 Mar 28 2026 09:24:59

%S 1,3,17,79,321,1211,4369,15303,52481,177139,590481,1948607,6377281,

%T 20726187,66961553,215233591,688747521,2195382755,6973568785,

%U 22082967855,69735688001,219667417243,690383311377,2165293112999,6778308875521,21182215236051,66088511536529

%N a(n) = n*(3^n - 1) + 1.

%C A sequence that occurs in A394330.

%H Paolo Xausa, <a href="/A394342/b394342.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,24,-9).

%F a(n) = A036290(n) + 1 - n.

%F a(n) = A050914(n) - n.

%F From _Stefano Spezia_, Mar 21 2026: (Start)

%F G.f.: (1 - 5*x + 15*x^2 - 15*x^3)/((1 - 3*x)^2*(1 - x)^2).

%F E.g.f.: exp(x)*(1 + (3*exp(2*x) - 1)*x). (End)

%t A394342[n_] := n*(3^n - 1) + 1; Array[A394342, 30, 0] (* or *)

%t LinearRecurrence[{8, -22, 24, -9}, {1, 3, 17, 79}, 30] (* _Paolo Xausa_, Mar 27 2026 *)

%Y Cf. A036290, A050914, A394330.

%K nonn,easy

%O 0,2

%A _A.H.M. Smeets_, Mar 17 2026