Search: id:A015530
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%I A015530
%S A015530 0,1,4,19,88,409,1900,8827,41008,190513,885076,4111843,19102600,
%T A015530 88745929,412291516,1915403851,8898489952,41340171361,192056155300,
%U A015530 892245135283,4145149007032,19257331433977,89464772757004
%N A015530 Linear 2nd order recurrence.
%C A015530 Let b(1)=1, b(k)=floor(b(k-1))+3/b(k-1); then for n>1, b(n)=a(n)/a(n-1). 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 09 2002
%C A015530 In general, x/(1-a*x-b*x^2) has a(n)=sum{k=0..floor((n-1)/2),C(n-k-1,
               k)b^k*a^(n-2k-1)}. - Paul Barry (pbarry(AT)wit.ie), Apr 23 2005
%F A015530 a(n) = 4 a(n-1) + 3 a(n-2).
%F A015530 G.f.: x/(1-4x-3x^2). a(n) = (A086901(n+2) - A086901(n+1))/6. - Ralf Stephan 
               (ralf(AT)ark.in-berlin.de), Feb 01 2004
%F A015530 a(n)=sum{k=0..floor((n-1)/2), C(n-k-1, k)3^k*4^(n-2k-1)} - Paul Barry 
               (pbarry(AT)wit.ie), Apr 23 2005
%F A015530 ((2+sqrt7)^n-(2-sqrt7)^n)/sqrt28. Offset 1. a(3)=19 [From Al Hakanson 
               (hawkuu(AT)gmail.com), Jan 05 2009]
%o A015530 (Other) sage: [lucas_number1(n,4,-3) for n in xrange(0, 23)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%Y A015530 Sequence in context: A017961 A017962 A084155 this_sequence A010907 A087449 
               A004253
%Y A015530 Adjacent sequences: A015527 A015528 A015529 this_sequence A015531 A015532 
               A015533
%K A015530 nonn,easy
%O A015530 0,3
%A A015530 Olivier Gerard (olivier.gerard(AT)gmail.com)

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