Search: id:A015537
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%I A015537
%S A015537 0,1,5,29,165,941,5365,30589,174405,994381,5669525,32325149,184303845,
%T A015537 1050819821,5991314485,34159851709,194764516485,1110461989261,
%U A015537 6331368012245,36098688018269,205818912140325,1173489312774701
%N A015537 Linear 2nd order recurrence.
%C A015537 First differences give A122690(n) = {1, 4, 24, 136, 776, 4424, 25224, 
               ...}. Partial sums of a(n) are {0, 1, 6, 35, 200, ...} = (A123270(n) 
               - 1)/8. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 03 2006
%F A015537 a(n) = 5 a(n-1) + 4 a(n-2).
%F A015537 a(n)=sum{k=0..floor((n-1)/2), C(n-k-1, k)4^k*5^(n-2k-1)} - Paul Barry 
               (pbarry(AT)wit.ie), Apr 23 2005
%F A015537 a(n) = Sum[ A122690(k), {k,0,n-1} ] for n>0. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 03 2006
%F A015537 a(n)=(1/41)*sqrt(41)*{[(5/2)+(1/2)*sqrt(41)]^n-[(5/2)-(1/2)*sqrt(41)]^n}, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jan 13 2009]
%o A015537 (Other) sage: [lucas_number1(n,5,-4) for n in xrange(0, 22)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
%Y A015537 Cf. A122690, A123270.
%Y A015537 Sequence in context: A060926 A098780 A146178 this_sequence A141812 A001653 
               A141814
%Y A015537 Adjacent sequences: A015534 A015535 A015536 this_sequence A015538 A015539 
               A015540
%K A015537 nonn,easy
%O A015537 0,3
%A A015537 Olivier Gerard (olivier.gerard(AT)gmail.com)

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