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 A172447 #36 Sep 08 2022 08:45:50
%S A172447 1,4,17,70,283,1136,4549,18202,72815,291268,1165081,4660334,18641347,
%T A172447 74565400,298261613,1193046466,4772185879,19088743532,76354974145,
%U A172447 305419896598,1221679586411,4886718345664,19546873382677,78187493530730,312749974122943,1250999896491796
%N A172447 a(n) = (-1 + 5*2^(2*n + 1) - 3*n)/9.
%C A172447 a(n) mod 10 gives the 10-periodic sequence 1, 4, 7, 0, 3, 6, 9, 2, 5, 8 (and repeat, A131579 shifted, A144468 reversed) which contains all ten digits, that has a "palindromic" symmetry: 1 + 8 = 4 + 5 = 7 + 2 = 0 + 9 = 3 + 6 = 9.
%C A172447 The inverse binomial transform gives 1, 3, 10, 30, 90, ... (A062107 shifted). - _R. J. Mathar_, Feb 11 2010
%H A172447 Vincenzo Librandi, <a href="/A172447/b172447.txt">Table of n, a(n) for n = 0..1000</a>
%H A172447 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F A172447 a(n) = 6*a(n - 1) - 9*a(n - 2) + 4*a(n - 3).
%F A172447 a(n + 1) - 4*a(n) = n.
%F A172447 a(n) = A172416(2n + 1).
%F A172447 G.f.: (1 - 2*x + 2*x^2)/((1 - 4*x) * (x - 1)^2). - _R. J. Mathar_, Feb 11 2010
%F A172447 E.g.f.: (10*exp(4*x) - (1 + 3*x)*exp(x))/9. - _G. C. Greubel_, Nov 02 2018
%t A172447 LinearRecurrence[{6, -9, 4}, {1, 4, 17}, 30] (* _Harvey P. Dale_, Mar 25 2016 *)
%t A172447 ((-1 + 5 2^(2# + 1) - 3#)/9 &) /@ Range[0, 29] (* _Alonso del Arte_, Apr 25 2020 *)
%o A172447 (Magma) [(-1+5*2^(2*n+1)-3*n)/9: n in [0..30]]; // _Vincenzo Librandi_, Aug 05 2011
%o A172447 (PARI) a(n)=(10*4^n-3*n)\9 \\ _Charles R Greathouse IV_, Jul 21 2015
%o A172447 (Scala) val powerOf2: LazyList[BigInt] = LazyList.iterate(1: BigInt)(_ * 2)
%o A172447 (0 to 29).map(n => (-1 + 5 * powerOf2(2 * n + 1) - 3 * n)/9) // _Alonso del Arte_, Apr 25 2020
%Y A172447 Cf. A072197 (first differences).
%K A172447 nonn,easy
%O A172447 0,2
%A A172447 _Paul Curtz_, Feb 03 2010
%E A172447 Definition replaced by closed formula by _R. J. Mathar_, Feb 11 2010