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 A172252 #25 Jun 16 2025 00:00:19
%S A172252 -1,7,23,55,119,247,503,1015,2039,4087,8183,16375,32759,65527,131063,
%T A172252 262135,524279,1048567,2097143,4194295,8388599,16777207,33554423,
%U A172252 67108855,134217719,268435447,536870903,1073741815,2147483639,4294967287,8589934583,17179869175,34359738359
%N A172252 a(n) = 4*2^n - 9.
%H A172252 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A172252 a(n) = 2*a(n-1) + 9, a(1)= -1. - _Vincenzo Librandi_, Mar 20 2011
%F A172252 For n >= 3, a(n) = 8<+>(n+2), where operation <+> is defined in A206853. - _Vladimir Shevelev_, Feb 17 2012
%F A172252 From _Elmo R. Oliveira_, Jun 15 2025: (Start)
%F A172252 G.f.: x*(10*x-1)/((x-1)*(2*x-1)).
%F A172252 E.g.f.: 5 + exp(x)*(4*exp(x) - 9).
%F A172252 a(n) = A185346(n+2) = 4*A000225(n) - 5.
%F A172252 a(n) = A159741(n-1) - 1 for n > 1. (End)
%t A172252 Table[4 2^n - 9, {n, 1, 100}]
%t A172252 LinearRecurrence[{3,-2},{-1,7},30] (* _Harvey P. Dale_, May 27 2021 *)
%o A172252 (PARI) my(x='x+O('x^34)); Vec(x*(10*x-1)/((x-1)*(2*x-1))) \\ _Elmo R. Oliveira_, Jun 15 2025
%Y A172252 Cf. A000225, A159741, A185346, A206853.
%K A172252 sign,easy
%O A172252 1,2
%A A172252 _Artur Jasinski_, Jan 29 2010
%E A172252 More terms from _Elmo R. Oliveira_, Jun 15 2025