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

0,3

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)

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

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 *)

Prog

(Sage) [lucas_number1(n, 2, -15) for n in range(0, 23)] # Zerinvary Lajos, Apr 22 2009
(Magma) [(5^n-(-3)^n)/8: n in [0..25]]; // Vincenzo Librandi, Aug 05 2013

Crossrefs

Cf. A051958, A015441.

Sequence in context: A365494 A232537 A309341 * A217082 A024220 A024389

Adjacent sequences: A079770 A079771 A079772 * A079774 A079775 A079776

Keyword

nonn,easy

Author

Paul Barry, Feb 20 2003

Status

approved