A079773 a(n) = 2*a(n-1)+15*a(n-2) with n>0, a(0)=0, a(1)=1.

0, 1, 2, 19, 68, 421, 1862, 10039, 48008, 246601, 1213322, 6125659, 30451148, 152787181, 762341582, 3816490879, 19068105488, 95383574161, 476788730642, 2384331073699, 11920493107028, 59605952319541, 298019301244502

Offset: 0

Author

Paul Barry, Feb 20 2003

Keywords

• nonn
• easy

References

• F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,15)

Crossrefs

Cf. A051958, A015441.

Programs

Magma

[(5^n-(-3)^n)/8: n in [0..25]]; // Vincenzo Librandi, Aug 05 2013

Mathematica

Join[{a=0,b=1},Table[c=2*b+15*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[x / ((1 + 3 x) (1 - 5 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)

Sage

[lucas_number1(n,2,-15) for n in range(0, 23)] # Zerinvary Lajos, Apr 22 2009

Formula

G.f.: x/((1+3*x)*(1-5*x)).

a(n) = (5^n-(-3)^n)/8.

a(n) = sum(k=1..n, binomial(n, 2*k-1)*4^(2*(k-1))).

E.g.f.: exp(x)*sinh(4*x)/4. - Paul Barry, Jul 09 2003

a(n+1) = Sum_{k = 0..n} A238801(n,k)*4^k. - Philippe Deléham, Mar 07 2014