A375966 Powers of 3 alternating with powers of 4.

1, 1, 3, 4, 9, 16, 27, 64, 81, 256, 243, 1024, 729, 4096, 2187, 16384, 6561, 65536, 19683, 262144, 59049, 1048576, 177147, 4194304, 531441, 16777216, 1594323, 67108864, 4782969, 268435456, 14348907, 1073741824, 43046721, 4294967296, 129140163, 17179869184

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-12).

Formula

a(n) = 7*a(n-2) - 12*a(n-4) for n >= 4.

From Stefano Spezia, Sep 06 2024: (Start)

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

a(n) = (4*3^(n/2)*A059841(n) - (-2)^n + 2^n)/4.

E.g.f.: cosh(sqrt(3)*x) + cosh(x)*sinh(x). (End)

Mathematica

seq[len_] := Module[{m = Ceiling[len/2] - 1}, Riffle @@ Map[#^Range[0, m] &, {3, 4}]]; seq[36] (* Amiram Eldar, Sep 05 2024 *)

Prog

(Python)
def A375966(n): return 1<<(n^1) if n&1 else 3**(n>>1) # Chai Wah Wu, Sep 24 2024

Crossrefs

Cf. A000244 and A000302 interleaved.

Cf. A000035, A059841, A072345, A098293.

Sequence in context: A336450 A372823 A367083 * A271785 A054188 A093368

Adjacent sequences: A375963 A375964 A375965 * A375967 A375968 A375969

Keyword

nonn,easy

Author

Paul Curtz, Sep 04 2024

Status

approved