A094375 a(n) = (4^n - 2^n)/2 + 3^n.

1, 4, 15, 55, 201, 739, 2745, 10315, 39201, 150499, 582825, 2273275, 8918001, 35144659, 138992505, 551203435, 2190497601, 8719009219, 34747027785, 138600952795, 553242074001, 2209482560179, 8827471984665, 35278511073355

Offset: 0

Author

Paul Barry, Apr 28 2004

Keywords

• easy
• nonn

Comments

Binomial transform of A094374.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

Crossrefs

Cf. A000244, A006516, A094374.

Programs

Magma

[2^(n-1)*(2^n -1) +3^n: n in [0..30]]; // G. C. Greubel, Sep 26 2024

Mathematica

LinearRecurrence[{9,-26,24}, {1,4,15}, 31] (* G. C. Greubel, Sep 26 2024 *)

SageMath

[(4^n +2*3^n -2^n)//2 for n in range(31)] # G. C. Greubel, Sep 26 2024

Formula

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

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

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

E.g.f.: exp(3*x)*(1 + sinh(x)). - G. C. Greubel, Sep 26 2024