A153180 - OEIS

%I #6 Mar 16 2017 12:18:10

%S 521,90481,35355581,10525900321,3489827263001,1111126318086721,

%T 359316586176453881,115509240442846111681,37216910406644366498621,

%U 11980863523543017476802001,3858153294795970321295258921

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

%C All numbers in this sequence are:

%C congruent to 1 mod 10

%C 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),

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

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (233, 33552, -1493064, -27372840, 186135312, 488605194, -488605194, -186135312, 27372840, 1493064, -33552, -233, 1).

%F a(n)= +233*a(n-1) +33552*a(n-2) -1493064*a(n-3) -27372840*a(n-4) +186135312*a(n-5) +488605194*a(n-6) -488605194*a(n-7) -186135312*a(n-8) +27372840*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]

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

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 20 2008