A153175 a(n) = L(7*n)/L(n) where L(n) = Lucas number A000204(n).

29, 281, 6119, 101521, 1875749, 33281921, 599786069, 10745088481, 192933544679, 3461223997001, 62114818827629, 1114566304366081, 20000347407134669, 358889844987430121, 6440029487834912999, 115561554399692896321

Offset: 1

Author

Artur Jasinski, Dec 20 2008

Keywords

• nonn

Comments

All numbers in this sequence are:

congruent to 9 mod 10 (iff n is odd),

congruent to 1 mod 10 (iff n is even).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..795
• Index entries for linear recurrences with constant coefficients, signature (13,104,-260,-260,104,13,-1).

Crossrefs

Cf. A000032, A000204, A110391, A153173.

Cf. A153177, A153179, A153180. [From R. J. Mathar, Oct 22 2010]

Programs

Magma

[Lucas(7*n)/Lucas(n): n in [0..30]]; // G. C. Greubel, Dec 21 2017

Mathematica

Table[LucasL[7*n]/LucasL[n], {n, 1, 50}]

PARI

{lucas(n) = fibonacci(n+1) + fibonacci(n-1)};
for(n=0,30, print1( lucas(7*n)/lucas(n), ", ")) \\ G. C. Greubel, Dec 21 2017

Formula

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

a(n) = +13*a(n-1) +104*a(n-2) -260*a(n-3) -260*a(n-4) +104*a(n-5) +13*a(n-6) -a(n-7).

G.f.: -x*(-29+96*x+550*x^2-290*x^3-200*x^4+16*x^5+x^6) / ( (1+x)*(x^2-3*x+1)*(x^2-18*x+1)*(x^2+7*x+1) ).

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