This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A097165 #8 Jun 13 2015 00:51:29
%S A097165 1,7,41,227,1221,6447,33601,173467,889181,4533287,23015961,116477907,
%T A097165 587981941,2962279327,14900875121,74862289547,375743103501,
%U A097165 1884442140567,9445117195081,47317211944387,236952563597861
%N A097165 Expansion of (1-3x)/((1-x)(1-4x)(1-5x)).
%C A097165 Partial sums of A085351. Convolution of A034478 and 4^n. Convolution of A047849 and 5^n. a(n)=A097162(2n+1)/3. Third binomial transform of A097164.
%H A097165 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-29,20).
%F A097165 a(n)=5*5^n/2-4*4^n/3-1/6; a(n)=sum{k=0..n, (5^k+1)4^(n-k)/2}; a(n)=sum{k=0..n, (4^k+2)5^(n-k)/3}; a(n)=10a(n-1)-29a(n-2)+20a(n-3).
%t A097165 CoefficientList[Series[(1-3x)/((1-x)(1-4x)(1-5x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-29,20},{1,7,41},30] (* _Harvey P. Dale_, Jan 24 2012 *)
%K A097165 easy,nonn
%O A097165 0,2
%A A097165 _Paul Barry_, Jul 30 2004