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 A134522 #23 Jun 14 2025 13:34:17
%S A134522 1,3,5,10,18,35,67,132,260,517,1029,2054,4102,8199,16391,32776,65544,
%T A134522 131081,262153,524298,1048586,2097163,4194315,8388620,16777228,
%U A134522 33554445,67108877,134217742,268435470,536870927,1073741839,2147483664,4294967312,8589934609
%N A134522 a(n) = 2^n + ceiling(n/2).
%H A134522 Andrew Howroyd, <a href="/A134522/b134522.txt">Table of n, a(n) for n = 0..500</a>
%H A134522 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F A134522 From _Andrew Howroyd_, Aug 10 2018: (Start)
%F A134522 a(n) = A000079(n) + A110654(n).
%F A134522 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
%F A134522 G.f.: (1 - 3*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 - 2*x)). (End)
%F A134522 a(n) = Sum_{k=1..n+1} C(n+1,k)^(k mod 2). - _Wesley Ivan Hurt_, Nov 20 2021
%F A134522 E.g.f.: (x*cosh(x) + 2*cosh(2*x) + (1 + x + 4*cosh(x))*sinh(x))/2. - _Stefano Spezia_, Jun 14 2025
%t A134522 CoefficientList[Series[(1 - 3*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 - 2*x)),{x,0,33}],x] (* _James C. McMahon_, Apr 07 2025 *)
%o A134522 (PARI) a(n)=2^n + (n+1)\2; \\ _Andrew Howroyd_, Aug 10 2018
%o A134522 (PARI) Vec((1 - 3*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ _Andrew Howroyd_, Aug 10 2018
%Y A134522 Row sums of A134521.
%Y A134522 Cf. A000079, A110654.
%K A134522 nonn,easy
%O A134522 0,2
%A A134522 _Gary W. Adamson_, Oct 29 2007
%E A134522 Name changed, a(8) inserted and a(14)-a(33) from _Andrew Howroyd_, Aug 10 2018