Search: id:A099432
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%I A099432
%S A099432 1,6,33,162,756,3402,14931,64314,273051,1145988,4764744,19656756,
%T A099432 80561061,328316814,1331513397,5377120038,21633427836,86747114430,
%U A099432 346810621815,1382826606210,5500378861551,21830478128136,86469557676048
%N A099432 Convolution of A030195(n) (generalized (3,3)-Fibonacci) with itself.
%F A099432 G.f.: 1/(1-3x-3x^2)^2; a(n)=6a(n-1)+3a(n-2)+18a(n-3)+9a(n-4); a(n)=sum{k=0..floor((n+2)/
               2), k*binomial(n-k+2, k)3^(n-k+1)}; a(n)=(sqrt(7)n+2sqrt(7)-sqrt(3))(5sqrt(7)/
               98+sqrt(3)/14)(3sqrt(21)/2 + 15/2)^(n/2) +(15/2-3sqrt(21)/2)^(n/2)(sqrt(7)n+2sqrt(7)+sqrt(3))(5sqrt(7)/
               98-sqrt(3)/14)(-1)^n.
%e A099432 sage: taylor( mul(x/(1 - 3*x - 3*x^2)^2 for i in xrange(1,2)),x,0,23)# 
               solution >>x + 6*x^2 + 33*x^3 + 162*x^4 + 756*x^5 +....+ 5500378861551*x^21 
               + 21830478128136*x^22 + 86469557676048*x^23 + etc... [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
%o A099432 (Other) sage: taylor( mul(x/(1 - 3*x - 3*x^2)^2 for i in xrange(1,2)),
               x,0,23)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 
               03 2009]
%Y A099432 Cf. A073388.
%Y A099432 Sequence in context: A120009 A074087 A022730 this_sequence A072260 A084153 
               A086314
%Y A099432 Adjacent sequences: A099429 A099430 A099431 this_sequence A099433 A099434 
               A099435
%K A099432 easy,nonn
%O A099432 0,2
%A A099432 Paul Barry (pbarry(AT)wit.ie), Oct 15 2004

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