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 A093140 #31 Aug 17 2024 14:26:08
%S A093140 1,5,45,445,4445,44445,444445,4444445,44444445,444444445,4444444445,
%T A093140 44444444445,444444444445,4444444444445,44444444444445,
%U A093140 444444444444445,4444444444444445,44444444444444445,444444444444444445,4444444444444444445,44444444444444444445,444444444444444444445
%N A093140 Expansion of (1-6*x)/((1-x)*(1-10*x)).
%C A093140 Second binomial transform of 4*A001045(3n)/3+(-1)^n. Partial sums of A093141. A convex combination of 10^n and 1. In general the second binomial transform of k*Jacobsthal(3n)/3+(-1)^n is 1, 1+k, 1+11k, 1+111k, ... This is the case for k=4.
%H A093140 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A093140 G.f.: (1-6*x)/((1-x)*(1-10*x)).
%F A093140 a(n) = 4*10^n/9 + 5/9.
%F A093140 a(n+1) = (A102807(n+1)-A002477(n))/((Sum_{i=1..n} 2*10^i) + 3). [_Roger L. Bagula_, May 22 2010]
%F A093140 a(n) = 10*a(n-1)-5 with a(0)=1. - _Vincenzo Librandi_, Aug 02 2010
%F A093140 a(n) = 11*a(n-1)-10*a(n-2). - _Wesley Ivan Hurt_, May 20 2021
%F A093140 E.g.f.: exp(x)*(4*exp(9*x) + 5)/9. - _Elmo R. Oliveira_, Aug 17 2024
%t A093140 CoefficientList[Series[(1-6x)/((1-x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{11,-10},{1,5},30] (* or *) Join[{1},Table[FromDigits[PadLeft[{5},n,4]],{n,30}]] (* _Harvey P. Dale_, Dec 17 2022 *)
%Y A093140 Cf. A001045, A002477, A093141, A102807.
%K A093140 easy,nonn
%O A093140 0,2
%A A093140 _Paul Barry_, Mar 24 2004
%E A093140 a(19)-a(22) from _Elmo R. Oliveira_, Aug 17 2024