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A153180 a(n) = L(13n)/L(n) where L(n) = Lucas number A000204(n). 3
521, 90481, 35355581, 10525900321, 3489827263001, 1111126318086721, 359316586176453881, 115509240442846111681, 37216910406644366498621, 11980863523543017476802001, 3858153294795970321295258921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..11.

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

FORMULA

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]

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A324630 A167734 A122715 * A173656 A015291 A028484

Adjacent sequences:  A153177 A153178 A153179 * A153181 A153182 A153183

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 20 2008

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)