%I A083100
%S A083100 1,9,25,113,401,1593,5993,23137,88225,338409,1294393,4957649,18976049,
%T A083100 72655641,278143625,1064876737,4076758849,15607654857,59752621657,
%U A083100 228758827313,875786006225,3352883803641,12836269650857,49142725927201
%N A083100 a(n)=2a(n-1)+7a(n-2).
%C A083100 a(n)=a(n-1)+8*A015519(n). a(n)/A015519(n+1) converges to sqrt(8).
%F A083100 G.f.: (1+7x)/(1-2x-7x^2)
%F A083100 a(n)=(1/2)*[1-2*sqrt(2)]^n+sqrt(2)*[1+2*sqrt(2)]^n-[1-2*sqrt(2)]^n*sqrt(2)+(1/
               2)*[1+2 *sqrt(2)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 
               10 2008
%F A083100 a(n)=binomial transform of 1,8,8,64,64,512 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Aug 17 2009]
%t A083100 CoefficientList[Series[(1 + 7 x)/(1 - 2 x - 7 x^2), {x, 0, 25}], x]
%Y A083100 Essentially a duplicate of A084058.
%Y A083100 The following sequences (and others) belong to the same family: A001333, 
               A000129, A026150, A002605, A046717, A015518, A084057, A063727, A002533, 
               A002532, A083098, A083099, A083100, A015519.
%Y A083100 Sequence in context: A147475 A146674 A083672 this_sequence A084058 A108570 
               A092769
%Y A083100 Adjacent sequences: A083097 A083098 A083099 this_sequence A083101 A083102 
               A083103
%K A083100 easy,nonn
%O A083100 0,2
%A A083100 Mario Catalani (mario.catalani(AT)unito.it), Apr 23 2003