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 A137215 #13 Jan 05 2022 17:34:55
%S A137215 3,32,355,4110,48887,588886,7111107,85555550,1022222215,12111111102,
%T A137215 142222222211,1655555555542,19111111111095,218888888888870,
%U A137215 2488888888888867,28111111111111086,315555555555555527,3522222222222222190,39111111111111111075,432222222222222222182
%N A137215 a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
%C A137215 Sequence generalized: a(n) = a(0)*(B^n) + F(n)* ((B^n)-1)/(B-1); a(0), B integers, F(n) arithmetic function.
%C A137215 Examples:
%C A137215 a(0) = 1, B = 10, F(n) = 1 gives A002275, F(n) = 2 gives A090843, F(n) = 3 gives A097166, F(n) = 4 gives A099914, F(n) = 5 gives A099915.
%C A137215 a(0) = 1, B = 2, F(n) = 1 gives A000225, F(n) = 2 gives A033484, F(n) = 3 gives A036563, F(n) = 4 gives A048487, F(n) = 5 gives A048488, F(n) = 6 gives A048489.
%C A137215 a(0) = 1, B = 3, F(n) = 1 gives A003462, F(n) = 2 gives A048473, F(n) = 3 gives A134931, F(n) = 4 gives A058481, F(n) = 5 gives A116952.
%C A137215 a(0) = 1, B = 4, F(n) = 1 gives A002450, F(n) = 2 gives A020989, F(n) = 3 gives A083420, F(n) = 4 gives A083597, F(n) = 5 gives A083584.
%C A137215 a(0) = 1, B = 5, F(n) = 1 gives A003463, F(n) = 2 gives A057651, F(n) = 3 gives A117617, F(n) = 4 gives A081655.
%C A137215 a(0) = 2, B = 10, F(n) = 1 gives A037559, F(n) = 2 gives A002276.
%H A137215 G. C. Greubel, <a href="/A137215/b137215.txt">Table of n, a(n) for n = 0..985</a>
%H A137215 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (33,-393,1991,-3930,3300,-1000).
%F A137215 a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
%F A137215 O.g.f.: (3 - 67*x + 478*x^2 - 1002*x^3 + 850*x^4 - 100*x^5)/((1-x)^3 * (1-10*x)^3). - _R. J. Mathar_, Mar 16 2008
%e A137215 a(3) = 3*10^3 + (3*3 + 1)*(10^3 - 1)/9 = 4110.
%t A137215 Table[3*10^n +(n^2 +1)*(10^n -1)/9, {n,0,30}] (* _G. C. Greubel_, Jan 05 2022 *)
%o A137215 (PARI) a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9; \\ _Jinyuan Wang_, Feb 27 2020
%o A137215 (Sage) [3*10^n +(1+n^2)*(10^n -1)/9 for n in (0..30)] # _G. C. Greubel_, Jan 05 2022
%Y A137215 Cf. A002275, A011557.
%K A137215 nonn,easy
%O A137215 0,1
%A A137215 _Ctibor O. Zizka_, Mar 06 2008
%E A137215 More terms from _R. J. Mathar_, Mar 16 2008
%E A137215 More terms from _Jinyuan Wang_, Feb 27 2020