A382675 - OEIS

%I #16 Mar 12 2026 18:26:14

%S 1,10,52,208,736,2440,7792,24328,74896,228520,693232,2095048,6315856,

%T 19009000,57149872,171695368,515577616,1547715880,4645113712,

%U 13939273288,41825684176,125492781160,376509800752,1129592316808,3388902779536,10166959996840,30501383306992,91505156553928

%N a(n) = 4 - 15 * 2^n + 12 * 3^n.

%H Paolo Xausa, <a href="/A382675/b382675.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

%F From _Stefano Spezia_, Mar 05 2026: (Start)

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

%F E.g.f.: exp(x)*(4 - 15*exp(x) + 12*exp(2*x)). (End)

%t A382675[n_] := 12*3^n - 15*2^n + 4; Array[A382675, 30, 0] (* or *)

%t LinearRecurrence[{6, -11, 6}, {1, 10, 52}, 30] (* _Paolo Xausa_, Mar 12 2026 *)

%o (PARI) a(n) = 4-15*2^n+12*3^n;

%Y Column k=2 of A382673.

%Y Row n=2 of A382673.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Apr 03 2025

%E More terms from _Paolo Xausa_, Mar 12 2026