A166481 a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.

1, 7, 3, 21, 9, 63, 27, 189, 81, 567, 243, 1701, 729, 5103, 2187, 15309, 6561, 45927, 19683, 137781, 59049, 413343, 177147, 1240029, 531441, 3720087, 1594323, 11160261, 4782969, 33480783, 14348907, 100442349, 43046721, 301327047

Offset: 1

Author

Klaus Brockhaus, Oct 14 2009

Keywords

• nonn

Comments

Interleaving of A000244 and A005032.

Seventh binomial transform is A153598.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (0,3).

Crossrefs

Cf. A000244 (powers of 3), A005032 (7*3^n), A153598.

Programs

Magma

[ n le 2 select 6*n-5 else 3*Self(n-2): n in [1..34] ];

Mathematica

LinearRecurrence[{0,3},{1,7},50] (* or *) Flatten[NestList[3#&,{1,7},20]] (* Harvey P. Dale, Sep 24 2015 *)

SageMath

def A166481(n): return 3^(n/2)*(sqrt(3)*(n%2) + 7*((n+1)%2))/3
[A166481(n) for n in range(1,41)] # G. C. Greubel, Aug 02 2024

Formula

a(n) = (5 + 2*(-1)^n)*3^((2*n - 5 + (-1)^n)/4).

G.f.: x*(1+7*x)/(1-3*x^2).

E.g.f.: (1/3)*(-7 + 7*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - G. C. Greubel, Aug 02 2024