A153180 a(n) = L(13n)/L(n) where L(n) = Lucas number A000204(n).

521, 90481, 35355581, 10525900321, 3489827263001, 1111126318086721, 359316586176453881, 115509240442846111681, 37216910406644366498621, 11980863523543017476802001, 3858153294795970321295258921

Offset: 1

Author

Artur Jasinski, Dec 20 2008

Keywords

• nonn

Comments

All numbers in this sequence are:

congruent to 1 mod 10

congruent to 1 mod 100 (iff n is congruent to 0 mod 5),Q congruent to 21 mod 100 (iff n is congruent to 1 or 4 mod 5),

congruent to 81 mod 100 (iff n is congruent to 2 or 3 mod 5).Q

Links

• Index entries for linear recurrences with constant coefficients, signature (233, 33552, -1493064, -27372840, 186135312, 488605194, -488605194, -186135312, 27372840, 1493064, -33552, -233, 1).

Crossrefs

A000032, A000204, A047221, A110391, A153173, A153175, A153177, A153179.

Programs

Mathematica

Table[LucasL[13 n]/LucasL[n], {n, 1, 150}]

Formula

a(n)= +233*a(n-1) +33552*a(n-2) -1493064*a(n-3) -27372840*a(n-4) [phone]*a(n-5) [phone]*a(n-6) -488605194*a(n-7) -186135312*a(n-8) [phone]*a(n-9) +1493064*a(n-10) -33552*a(n-11) -233*a(n-12) +a(n-13). G.f.: -1+ (-2-123*x)/(x^2+123*x+1) +(2-322*x)/(x^2-322*x+1) +(-2-3*x)/(x^2+3*x+1) +(2-7*x)/(x^2-7*x+1) +(2-47*x)/(x^2-47*x+1) -1/(x-1)+ (-2-18*x)/(x^2+18*x+1). [From R. J. Mathar, Oct 22 2010]