A166984 a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 20.

1, 20, 336, 5440, 87296, 1397760, 22368256, 357908480, 5726601216, 91625881600, 1466015154176, 23456246661120, 375299963355136, 6004799480791040, 96076791961092096, 1537228672451215360, 24595658763514413056, 393530540233410478080, 6296488643803287126016

Offset: 0

Author

Klaus Brockhaus, Oct 26 2009

Keywords

• nonn
• easy

Comments

Partial sums of A166965.

First differences of A006105. - Klaus Purath, Oct 15 2020

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..830 (terms 0..200 from Vincenzo Librandi)
• E. Saltürk and I. Siap, Generalized Gaussian Numbers Related to Linear Codes over Galois Rings, European Journal of Pure and Applied Mathematics, Vol. 5, No. 2, 2012, 250-259; ISSN 1307-5543. - From _N. J. A. Sloane_, Oct 23 2012
• Index entries for linear recurrences with constant coefficients, signature (20,-64).

Crossrefs

Cf. A000302, A002450, A002452, A002453, A006105, A079598, A083584.

Cf. A115490, A166914, A166917, A166927, A166965, A307695.

Programs

Magma

[n le 2 select 19*n-18 else 20*Self(n-1)-64*Self(n-2): n in [1..17] ];

Mathematica

LinearRecurrence[{20,-64},{1,20},30] (* Harvey P. Dale, Jul 04 2012 *)

PARI

a(n) = (4*16^n - 4^n)/3 \\ Charles R Greathouse IV, Jun 21 2022

SageMath

A166984=BinaryRecurrenceSequence(20,-64,1,20)
[A166984(n) for n in range(31)] # G. C. Greubel, Oct 02 2024

Formula

a(n) = (4*16^n - 4^n)/3.

G.f.: 1/((1-4*x)*(1-16*x)).

Limit_{n -> oo} a(n)/a(n-1) = 16.

a(n) = A115490(n+1)/3.

Sum_{n>=0} a(n) x^(2*n+4)/(2*n+4)! = ( sinh(x) )^4/4!. - Robert A. Russell, Apr 03 2013

From Klaus Purath, Oct 15 2020: (Start)

a(n) = A002450(n+1)*(A002450(n+2) - A002450(n))/5.

a(n) = (A083584(n+1)^2 - A083584(n)^2)/80. (End)

a(n) = (A079598(n) - A000302(n))/24. - César Aguilera, Jun 21 2022

a(n) = 16*a(n-1) + 4^n with a(0) = 1. - Nadia Lafreniere, Aug 08 2022

E.g.f.: (4/3)*exp(10*x)*sinh(6*x + log(2)). - G. C. Greubel, Oct 02 2024