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 A016169 #34 Nov 10 2024 05:20:07
%S A016169 0,1,13,127,1105,9031,70993,543607,4085185,30275911,222009073,
%T A016169 1614529687,11664504865,83828316391,599858908753,4277376525367,
%U A016169 30411820662145,215703854542471,1526853641242033,10789535445362647
%N A016169 a(n) = 7^n - 6^n.
%C A016169 a(n) is also the number of n-digit numbers whose smallest decimal digit is 3. - _Stefano Spezia_, Nov 15 2023
%H A016169 G. C. Greubel, <a href="/A016169/b016169.txt">Table of n, a(n) for n = 0..1000</a>
%H A016169 John Elias, <a href="/A016169/a016169.png">Illustration of initial terms: a star number fractal</a>
%H A016169 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-42).
%F A016169 G.f.: x/((1-6*x)*(1-7*x)).
%F A016169 E.g.f.: exp(7*x) - exp(6*x). - _Mohammad K. Azarian_, Jan 14 2009
%F A016169 a(0)=0, a(n) = 7*a(n-1) + 6^(n-1). - _Vincenzo Librandi_, Feb 09 2011
%F A016169 a(0)=0, a(1)=1, a(n) = 13*a(n-1) - 42*a(n-2). - _Vincenzo Librandi_, Feb 09 2011
%p A016169 a:=n->sum(6^(n-j)*binomial(n,j),j=1..n): seq(a(n), n=0..30); # _Zerinvary Lajos_, Apr 18 2009
%t A016169 Table[7^n-6^n,{n,0,30}] (* or *) LinearRecurrence[{13,-42},{0,1},30] (* _Harvey P. Dale_, Apr 25 2020 *)
%o A016169 (Magma) [n le 2 select n-1 else 13*Self(n-1) -42*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 10 2024
%o A016169 (SageMath)
%o A016169 A016169=BinaryRecurrenceSequence(13,-42,0,1)
%o A016169 [A016169(n) for n in range(41)] # _G. C. Greubel_, Nov 10 2024
%Y A016169 Cf. A005062, A016177, A016189, A081201.
%K A016169 nonn,easy
%O A016169 0,3
%A A016169 _N. J. A. Sloane_