A051958 a(n) = 2*a(n-1) + 24*a(n-2), a(0)=0, a(1)=1.

0, 1, 2, 28, 104, 880, 4256, 29632, 161408, 1033984, 5941760, 36699136, 216000512, 1312780288, 7809572864, 47125872640, 281681494016, 1694383931392, 10149123719168, 60963461791744, 365505892843520, 2194134868688896

Offset: 0

Author

Barry E. Williams, Jan 04 2000

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
• Index entries for linear recurrences with constant coefficients, signature (2,24).

Crossrefs

Cf. A015441, A238801.

Programs

Magma

[(6^n-(-4)^n)/10: n in [0..30]]; // Vincenzo Librandi, Mar 08 2014

Mathematica

Table[(6^n-(-4)^n)/10, {n,0,30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[x/((1+4 x) (1-6 x)), {x,0,30}], x] (* Vincenzo Librandi, Mar 08 2014 *)
LinearRecurrence[{2,24},{0,1},30] (* Harvey P. Dale, May 08 2022 *)

PARI

a(n)=(6^n-(-4)^n)/10

SageMath

A051958=BinaryRecurrenceSequence(2,24,0,1)
[A051958(n) for n in range(31)] # G. C. Greubel, Nov 11 2024

Formula

G.f.: x/((1+4*x)*(1-6*x)).

a(n) = (6^n - (-4)^n)/10.

a(n) = 2^(n-1)*A015441(n).

a(n+1) = Sum_{k = 0..n} A238801(n,k)*5^k. - Philippe Deléham, Mar 07 2014

Limit_{n -> oo} a(n+1)/a(n) = 6. - Felix P. Muga II, Mar 10 2014

E.g.f.: (1/10)*(exp(6*x) - exp(-4*x)). - G. C. Greubel, Nov 11 2024