Search: id:A098347
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%I A098347
%S A098347 1,5,16,60,213,771,2772,9990,35973,129573,466668,1680804,6053697,
%T A098347 21803499,78529176,282836934,1018687833,3668986773,13214513016,
%U A098347 47594435868,171419886333,617399427555,2223674634060,8008962525846
%N A098347 A sequence derived from a Ferrers graph partition of 16.
%C A098347 One of the partitions of 16 is 5+5+2+2+1. Convert this Ferrers graph 
               representation to a 5 X 5 binary matrix.
%C A098347 Lim_{n->inf.} = 3.60167913188315425246437..., the characteristic polynomial 
               of m & m^-1 is x^5-3x^4-3x^3+3x^2 and its only positive root is the 
               limit.
%F A098347 a(1)=1, a(2)=5, a(3)=16, a(n)= 3a(n-1) + 3a(n-2) - 3a(n-3).
%e A098347 a(4)=60 because m^4.{1,0,0,0,0} = {60, 60, 45, 32, 16} and the first 
               or second element is 60.
%t A098347 a[1] = 1; a[2] = 5; a[3] = 16; a[n_] := a[n] = 3a[n - 1] + 3a[n - 2] 
               - 3a[n - 3]; Table[ a[n], {n, 24}] (* Or *)
%t A098347 m = {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 0, 0}, {1, 1, 0, 0, 
               0}, {1, 0, 0, 0, 0}}; Table[(MatrixPower[m, n].{1, 0, 0, 0, 0})[[1]], 
               {n, 24}]
%Y A098347 Sequence in context: A116914 A047103 A077235 this_sequence A034532 A092497 
               A026525
%Y A098347 Adjacent sequences: A098344 A098345 A098346 this_sequence A098348 A098349 
               A098350
%K A098347 nonn
%O A098347 1,2
%A A098347 Gary W. Adamson (qntmpkt(AT)yahoo.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 03 2004

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