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 A269059 #24 Mar 03 2024 19:04:16
%S A269059 1,6,19,48,113,258,579,1284,2821,6150,13319,28680,61449,131082,278539,
%T A269059 589836,1245197,2621454,5505039,11534352,24117265,50331666,104857619,
%U A269059 218103828,452984853,939524118,1946157079,4026531864,8321499161,17179869210,35433480219,73014444060
%N A269059 Construct a hollow square of 1's of side n and fill its interior with 0's to create a stack of n binary numbers. Express the sum of the stack in decimal.
%H A269059 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6, -13, 12, -4).
%F A269059 a(n) = 2*(2^n-1)+(n-2)*(2^(n-1)+1), for n>1.
%F A269059 G.f.: x*(1-2*x^2)^2/((1-2*x)^2*(1-x)^2). - _Robert Israel_, Feb 18 2016
%e A269059 1 1 1 3 1 1 1 7 1 1 1 1 15
%e A269059 a(1)=1 1 1 +3 1 0 1 +5 1 0 0 1 + 9
%e A269059 a(2)=6 1 1 1 +7 1 0 0 1 + 9
%e A269059 a(3)=19 1 1 1 1 +15
%e A269059 a(4)=48
%t A269059 Join[{1}, LinearRecurrence[{6, -13, 12, -4}, {0, 6, 19, 48}, {2, 32}]] (* _Jean-François Alcover_, Feb 27 2016 *)
%o A269059 (Magma) [1] cat [2*(2^n-1)+(n-2)*(2^(n-1)+1): n in [2..40]]; // _Vincenzo Librandi_, Feb 27 2016
%o A269059 (PARI) a(n) = if (n==1, 1, 2*(2^n-1)+(n-2)*(2^(n-1)+1)); \\ _Michel Marcus_, Mar 24 2016
%o A269059 (PARI) Vec(x*(1-2*x^2)^2/((1-2*x)^2*(1-x)^2) + O(x^100)) \\ _Altug Alkan_, Mar 24 2016
%K A269059 nonn,base,easy
%O A269059 1,2
%A A269059 _Gil Broussard_, Feb 18 2016