A153179 a(n) = L(11*n)/L(n) where L(n) = A000204(n).

199, 13201, 1970299, 224056801, 28374454999, 3450736132801, 426236170575799, 52337681992411201, 6441140796368008699, 792018481913198430001, 97420733208491869044199, 11981539981561372141075201

Offset: 1

Author

Artur Jasinski, Dec 20 2008

Keywords

• nonn

Comments

All numbers in this sequence are:

congruent to 99 mod 100 (iff n is odd),

congruent to 1 mod 100 (iff n is even).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..475
• Index entries for linear recurrences with constant coefficients, signature (89,4895,-83215,-582505,1514513,1514513,-582505,-83215,4895,89,-1).

Crossrefs

Cf. A000032, A000204, A110391, A153173, A153175, A153177.

Programs

Magma

[Lucas(11*n)/Lucas(n): n in [0..30]]; // G. C. Greubel, Dec 21 2017

Mathematica

Table[LucasL[11*n]/LucasL[n], {n, 1, 50}]

PARI

{lucas(n) = fibonacci(n+1) + fibonacci(n-1)};
for(n=0,30, print1( lucas(11*n)/lucas(n), ", ")) \\ G. C. Greubel, Dec 21 2017

Formula

From R. J. Mathar, Oct 22 2010: (Start)

a(n) = +89*a(n-1) +4895*a(n-2) -83215*a(n-3) -582505*a(n-4) +1514513*a(n-5) +1514513*a(n-6) -582505*a(n-7) -83215*a(n-8) +4895*a(n-9) +89*a(n-10) -a(n-11).

G.f.: -1 -1/(1+x) +(-2-47*x)/(x^2+47*x+1) +(2-3*x)/(x^2-3*x+1) +(-2-7*x)/(x^2+7*x+1) +(2-123*x)/(x^2-123*x+1) +(2-18*x)/(x^2-18*x+1).

a(n) = -(-1)^n -(-1)^n*A087265(n) +A005248(n) -(-1)^n*A056854(n) +A065705(n) +A087215(n). (End)