A200069 a(n) = 4*a(n-1) + 13*a(n-2) for n>2, a(1)=1, a(2)=4.

1, 4, 29, 168, 1049, 6380, 39157, 239568, 1467313, 8983636, 55009613, 336825720, 2062427849, 12628445756, 77325345061, 473471175072, 2899114186081, 17751582020260, 108694812500093, 665549816263752, 4075231827556217, 24953074921653644, 152790313444845397

Offset

1,2

Comments

De Moivres formula : a(n)=(r^n-s^n)/(r-s), for r>s gives sequences with integers if r and s are conjugates. With r=2+sqrt(17) and s=2-sqrt(17), a(n+1)/a(n) converges to 2+sqrt(17).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,13).

Formula

a(n) = ((2+sqrt(17))^n-(2-sqrt(17))^n)/(2*sqrt(17)).

G.f.: x/(1-4*x-13*x^2). - Bruno Berselli, Nov 15 2011

Example

a(3) = 4*4+13*1 = 29.

Mathematica

LinearRecurrence[{4, 13}, {1, 4}, 50]

Prog

(Haskell)
a200069 n = a200069_list !! (n-1)
a200069_list = 1 : 4 : zipWith (+)
   (map (* 4) $ tail a200069_list) (map (* 13) a200069_list)
-- Reinhard Zumkeller, Nov 15 2011

Crossrefs

Cf. A041025.

Sequence in context: A326100 A273209 A273271 * A302803 A300806 A303464

Adjacent sequences: A200066 A200067 A200068 * A200070 A200071 A200072

Keyword

nonn,easy

Author

Sture Sjöstedt, Nov 13 2011

Extensions

More terms from Bruno Berselli, Nov 15 2011

Status

approved