A015528 a(n) = 3*a(n-1) + 10*a(n-2).

0, 1, 3, 19, 87, 451, 2223, 11179, 55767, 279091, 1394943, 6975739, 34876647, 174387331, 871928463, 4359658699, 21798260727, 108991369171, 544956714783, 2724783836059, 13623918656007, 68119594328611, 340597969545903

Offset

0,3

Comments

The ratio a(n+1)/a(n) converges to 5 as n approaches infinity. - Felix P. Muga II, Mar 10 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014.

Index entries for linear recurrences with constant coefficients, signature (3, 10).

Formula

a(n) = 3*a(n-1) + 10*a(n-2).

a(n) = (5^n - (-2)^n)/7. Binomial transform is A015540. - Paul Barry, Feb 07 2004

G.f.: x/(1-x*(10*x+3)). - Harvey P. Dale, Jan 27 2012

Mathematica

Join[{a=0, b=1}, Table[c=3*b+10*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{3, 10}, {0, 1}, 30] (* or *) CoefficientList[Series[x/(1-x (10x+3)), {x, 0, 29}], x] (* Harvey P. Dale, Jan 27 2012 *)

Prog

(Sage) [lucas_number1(n, 3, -10) for n in range(0, 23)]# Zerinvary Lajos, Apr 22 2009
(Magma) [5^n/7-(-2)^n/7: n in [0..30]]; // Vincenzo Librandi, Aug 23 2011
(PARI) for(n=0, 30, print1((5^n - (-2)^n)/7, ", ")) \\ G. C. Greubel, Jan 01 2018

Crossrefs

Sequence in context: A373681 A089621 A204256 * A183384 A050863 A376836

Adjacent sequences: A015525 A015526 A015527 * A015529 A015530 A015531

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved