%I #12 Sep 27 2024 09:27:43

%S 1,4,15,55,201,739,2745,10315,39201,150499,582825,2273275,8918001,

%T 35144659,138992505,551203435,2190497601,8719009219,34747027785,

%U 138600952795,553242074001,2209482560179,8827471984665,35278511073355

%N a(n) = (4^n - 2^n)/2 + 3^n.

%C Binomial transform of A094374.

%H G. C. Greubel, <a href="/A094375/b094375.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).

%F G.f.: (1-5*x+5*x^2)/((1-2*x)*(1-3*x)*(1-4*x)).

%F a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3).

%F a(n) = A006516(n) + A000244(n).

%F E.g.f.: exp(3*x)*(1 + sinh(x)). - _G. C. Greubel_, Sep 26 2024

%t LinearRecurrence[{9,-26,24}, {1,4,15}, 31] (* _G. C. Greubel_, Sep 26 2024 *)

%o (Magma) [2^(n-1)*(2^n -1) +3^n: n in [0..30]]; // _G. C. Greubel_, Sep 26 2024

%o (SageMath) [(4^n +2*3^n -2^n)//2 for n in range(31)] # _G. C. Greubel_, Sep 26 2024

%Y Cf. A000244, A006516, A094374.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 28 2004