A087404 a(n) = 4a(n-1) + 5a(n-2).

2, 4, 26, 124, 626, 3124, 15626, 78124, 390626, 1953124, 9765626, 48828124, 244140626, 1220703124, 6103515626, 30517578124, 152587890626, 762939453124, 3814697265626, 19073486328124, 95367431640626, 476837158203124

Offset

0,1

Comments

Let F(x) = Product_{n>=0} (1 - x^(3*n+1))/(1 - x^(3*n+2)). This sequence is the simple continued fraction expansion of the real number 1 + F(-1/5) = 2.24761 97788 60361 46849 ... = 2 + 1/(4 + 1/(26 + 1/(124 + 1/(626 + ...)))). See A111317. - Peter Bala, Dec 26 2012

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (4, 5).

Formula

G.f.: (2 - 4*x)/(1 - 4*x - 5*x^2).

a(n) = 5^n + (-1)^n.

Mathematica

CoefficientList[Series[(2 - 4x)/(1 - 4x - 5x^2), {x, 0, 25}], x]
LinearRecurrence[{4, 5}, {2, 4}, 30] (* Harvey P. Dale, May 13 2022 *)

Prog

(Sage) [lucas_number2(n, 4, -5) for n in range(0, 22)] # Zerinvary Lajos, May 14 2009

Crossrefs

Cf. A111317.

Sequence in context: A144691 A367428 A085700 * A009237 A019019 A215882

Adjacent sequences: A087401 A087402 A087403 * A087405 A087406 A087407

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2003

Status

approved