A162436 a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 3.

1, 3, 3, 9, 9, 27, 27, 81, 81, 243, 243, 729, 729, 2187, 2187, 6561, 6561, 19683, 19683, 59049, 59049, 177147, 177147, 531441, 531441, 1594323, 1594323, 4782969, 4782969, 14348907, 14348907, 43046721, 43046721, 129140163, 129140163, 387420489, 387420489, 1162261467

Offset

1,2

Comments

Interleaving of A000244 and 3*A000244.

Unsigned version of A128019.

Partial sums are in A164123.

Apparently a(n) = A056449(n-1) for n > 1. a(n) = A108411(n) for n >= 1.

Binomial transform is A026150 without initial 1, second binomial transform is A001834, third binomial transform is A030192, fourth binomial transform is A161728, fifth binomial transform is A162272.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,3).

Formula

a(n) = 3^((1/4)*(2*n - 1 + (-1)^n)).

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

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

E.g.f.: cosh(sqrt(3)*x) - 1 + sinh(sqrt(3)*x)/sqrt(3). - Stefano Spezia, Dec 31 2022

Mathematica

CoefficientList[Series[(-3*x - 1)/(3*x^2 - 1), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
Transpose[NestList[{Last[#], 3*First[#]}&, {1, 3}, 40]][[1]] (* or *) With[{c= 3^Range[20]}, Join[{1}, Riffle[c, c]]](* Harvey P. Dale, Feb 17 2012 *)

Prog

(Magma) [ n le 2 select 2*n-1 else 3*Self(n-2): n in [1..35] ];
(PARI) a(n)=3^(n>>1) \\ Charles R Greathouse IV, Jul 15 2011

Crossrefs

Cf. A000244 (powers of 3), A128019 (expansion of (1-3x)/(1+3x^2)), A164123, A026150, A001834, A030192, A161728, A162272.

Essentially the same as A056449 (3^floor((n+1)/2)) and A108411 (powers of 3 repeated).

Sequence in context: A128019 A056449 A108411 * A146788 A147244 A146575

Adjacent sequences: A162433 A162434 A162435 * A162437 A162438 A162439

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 03 2009, Jul 05 2009

Extensions

G.f. corrected, formula simplified, comments added by Klaus Brockhaus, Sep 18 2009

Status

approved