A258439 Powers of 3 alternating with powers of 2.

1, 1, 3, 2, 9, 4, 27, 8, 81, 16, 243, 32, 729, 64, 2187, 128, 6561, 256, 19683, 512, 59049, 1024, 177147, 2048, 531441, 4096, 1594323, 8192, 4782969, 16384, 14348907, 32768, 43046721, 65536, 129140163, 131072, 387420489, 262144, 1162261467

Offset: 0

Author

Luce ETIENNE, May 30 2015

Keywords

• nonn
• easy

Comments

a(n)*A098293(n) = A000400(floor(n/2)).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-6).

Crossrefs

Cf. A098293, A006899.

Programs

GAP

Flat(List([0..20],n->[3^n,2^n])); # Muniru A Asiru, Jul 16 2018

Magma

&cat[[3^n, 2^n]: n in [0..35]]; // Vincenzo Librandi, Jul 17 2018

Maple

seq(op([3^n,2^n]),n=0..20); # Muniru A Asiru, Jul 16 2018

Mathematica

Flatten[Table[{3^n, 2^n}, {n, 0, 25}]] (* Vincenzo Librandi, Jul 17 2018 *)

PARI

Vec(-(3*x^3+2*x^2-x-1)/((2*x^2-1)*(3*x^2-1)) + O(x^100)) \\ Colin Barker, May 30 2015

Formula

a(n) = ((5+(-1)^n)/2)^((2*n-1+(-1)^n)/4).

a(n) = 5*a(n-2)-6*a(n-4). - Colin Barker, May 30 2015

G.f.: -(3*x^3+2*x^2-x-1) / ((2*x^2-1)*(3*x^2-1)). - Colin Barker, May 30 2015