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 A138894 #22 Sep 08 2022 08:45:33
%S A138894 1,11,101,911,8201,73811,664301,5978711,53808401,484275611,4358480501,
%T A138894 39226324511,353036920601,3177332285411,28595990568701,
%U A138894 257363915118311,2316275236064801,20846477124583211,187618294121248901
%N A138894 Expansion of (1+x)/(1-10*x+9*x^2).
%C A138894 Orbit starting at 1 of A138893: a(n)=A138893^(n)(1). Partial sums of A003952.
%C A138894 Sum of n-th row of triangle of powers of 9: 1; 1 9 1; 1 9 81 9 1; 1 9 81 729 81 9 1; ... - _Philippe Deléham_, Feb 22 2014
%H A138894 Vincenzo Librandi, <a href="/A138894/b138894.txt">Table of n, a(n) for n = 0..500</a>
%H A138894 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A138894 G.f.: (1+x)/((1-x)*(1-9x)).
%F A138894 a(n) = (5/4)*9^n - 1/4.
%F A138894 a(n) = A002452(n) + A002452(n+1).
%F A138894 Bisection of A135522/3. a(n+1)=9*a(n)+2. - _Paul Curtz_, Apr 22 2008
%F A138894 a(n) = Sum_{k=0..n} A112468(n,k)*10^k. - _Philippe Deléham_, Feb 22 2014
%e A138894 a(0) = 1;
%e A138894 a(1) = 1 + 9 + 1 = 11;
%e A138894 a(2) = 1 + 9 + 81 + 9 + 1 = 101;
%e A138894 a(3) = 1 + 9 + 81 + 729 + 81 + 9 + 1 = 911; etc. - _Philippe Deléham_, Feb 22 2014
%t A138894 Table[(5*9^n - 1)/4, {n, 0, 18}] (* _L. Edson Jeffery_, Feb 13 2015 *)
%o A138894 (Magma) [(5/4)*9^n-1/4: n in [0..20]]; // _Vincenzo Librandi_, Aug 09 2011
%o A138894 (PARI) Vec((1+x)/(1-10*x+9*x^2) + O(x^30)) \\ _Michel Marcus_, Feb 13 2015
%Y A138894 Cf. A096053 ((3*9^n-1)/2), a(n+1)=9a(n)-4 in A135423.
%Y A138894 Cf. A002452, A003952, A135522, A138893.
%K A138894 easy,nonn
%O A138894 0,2
%A A138894 _Paul Barry_, Apr 02 2008