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A094375
a(n) = (4^n - 2^n)/2 + 3^n.
1
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
0,2
COMMENTS
Binomial transform of A094374.
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
MATHEMATICA
LinearRecurrence[{9, -26, 24}, {1, 4, 15}, 31] (* G. C. Greubel, Sep 26 2024 *)
PROG
(Magma) [2^(n-1)*(2^n -1) +3^n: n in [0..30]]; // 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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 28 2004
STATUS
approved