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 A295089 #40 Sep 02 2025 14:12:17
%S A295089 3,7,17,33,55,83,117,157,203,255,313,377,447,523,605,693,787,887,993,
%T A295089 1105,1223,1347,1477,1613,1755,1903,2057,2217,2383,2555,2733,2917,
%U A295089 3107,3303,3505,3713,3927,4147,4373,4605,4843,5087,5337,5593,5855,6123,6397,6677,6963,7255,7553,7857
%N A295089 a(n) = 3*n^2 + n + 3.
%C A295089 Numbers represented as the palindrome 313 in number base n including base n=1, base 2 (binary) and base 3 with 'illegal' digit 3: 313_1=7, 313_2=17, 313_3=33, ... 313_9=255, 313_10=313, ...
%H A295089 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A295089 a(n) = A131649(n+3) + 1, n >= 2 (conjectured).
%F A295089 a(n) = A056108(n) + 2 = A049451(n) + 3 = A144391(n) + 4.
%F A295089 From _Elmo R. Oliveira_, Sep 02 2025: (Start)
%F A295089 G.f.: (3 - 2*x + 5*x^2)/(1-x)^3.
%F A295089 E.g.f.: (3 + 4*x + 3*x^2)*exp(x).
%F A295089 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%e A295089 313 in base 7 is 3*7^2 + 1*7 + 3 = 157.
%t A295089 Array[3 #^2 + # + 3 &, 52, 0] (* _Michael De Vlieger_, Nov 15 2017 *)
%t A295089 LinearRecurrence[{3, -3, 1}, {3, 7, 17}, 52] (* or *)
%t A295089 CoefficientList[Series[-(5 x^2 - 2 x + 3)/(x - 1)^3, {x, 0, 51}], x] (* _Robert G. Wilson v_, Nov 29 2017 *)
%o A295089 (PARI) a(n) = 3*n^2 + n + 3; \\ _Michel Marcus_, Dec 15 2017
%Y A295089 Cf. A049451, A056108, A131649, A144391.
%K A295089 nonn,easy,changed
%O A295089 0,1
%A A295089 _Ron Knott_, Nov 14 2017