A164737 a(n) = 8*a(n-2) for n > 2; a(1) = 5, a(2) = 12.

5, 12, 40, 96, 320, 768, 2560, 6144, 20480, 49152, 163840, 393216, 1310720, 3145728, 10485760, 25165824, 83886080, 201326592, 671088640, 1610612736, 5368709120, 12884901888, 42949672960, 103079215104, 343597383680, 824633720832

Offset

1,1

Comments

Interleaving of 5*A001018 and 12*A001018.

Binomial transform is A096980 without initial terms 1. Second binomial transform is A164593. Third binomial transform is A101386.

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,8).

Formula

a(n) = (13 - 7*(-1)^n)*2^(1/4*(6*n - 11 + 3*(-1)^n)).

G.f.: x*(5 + 12*x)/(1 - 8*x^2).

Maple

seq(coeff(series( x*(5+12*x)/(1-8*x^2) , x, n+1), x, n), n=1..30); # G. C. Greubel, Apr 16 2020

Mathematica

LinearRecurrence[{0, 8}, {5, 12}, 30] (* G. C. Greubel, Apr 16 2020 *)

Prog

(Magma) [ n le 2 select 7*n-2 else 8*Self(n-2): n in [1..26] ];
(SageMath) [(13 -7*(-1)^n)*2^((6*n -11 +3*(-1)^n)/4) for n in (1..30)] # G. C. Greubel, Apr 16 2020
(PARI) a(n)=([0, 1; 8, 0]^(n-1)*[5; 12])[1, 1] \\ Charles R Greathouse IV, May 20 2026
(PARI) a(n)=(13-7*(-1)^n)*2^(1/4*(6*n-11+3*(-1)^n)) \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A001018 (powers of 8), A067412, A096980, A101386, A164593.

Sequence in context: A233007 A221795 A092772 * A120779 A082189 A129795

Adjacent sequences: A164734 A164735 A164736 * A164738 A164739 A164740

Keyword

nonn,easy

Author

Klaus Brockhaus, Aug 24 2009

Status

approved