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 A293169 #15 Apr 10 2022 13:18:38
%S A293169 1,1,1,1,1,1,1,2,8,29,85,211,463,925,1718,3017,5097,8464,14197,24753,
%T A293169 45697,89150,180254,368734,748924,1493990,2914906,5565127,10434412,
%U A293169 19322901,35583926,65615746,121847272,228638698,433747259,830227401,1597653852,3078928619,5922703731,11347651254
%N A293169 a(n) = Sum_{k=0..n} binomial(k, 6*(n-k)).
%H A293169 Colin Barker, <a href="/A293169/b293169.txt">Table of n, a(n) for n = 0..1000</a>
%H A293169 V. E. Hoggatt, Jr., <a href="/A005676/a005676.pdf">7-page typed letter to N. J. A. Sloane with suggestions for new sequences</a>, circa 1977.
%H A293169 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1,1).
%F A293169 From _Colin Barker_, Oct 17 2017: (Start)
%F A293169 G.f.: (1 - x)^5 / (1 - 6*x + 15*x^2 - 20*x^3 + 15*x^4 - 6*x^5 + x^6 - x^7).
%F A293169 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) + a(n-7) for n>6.
%F A293169 (End)
%p A293169 f:=n-> add( binomial(k, 6*(n-k)), k=0..n);
%p A293169 [seq(f(n),n=0..30)];
%t A293169 Table[Sum[Binomial[k,6(n-k)],{k,0,n}],{n,0,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1,1},{1,1,1,1,1,1,1},50] (* _Harvey P. Dale_, Apr 10 2022 *)
%o A293169 (PARI) Vec((1 - x)^5 / (1 - 6*x + 15*x^2 - 20*x^3 + 15*x^4 - 6*x^5 + x^6 - x^7) + O(x^30)) \\ _Colin Barker_, Oct 18 2017
%Y A293169 Cf. A005676, A099132.
%K A293169 nonn,easy
%O A293169 0,8
%A A293169 _N. J. A. Sloane_, Oct 17 2017