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 A323988 #22 Dec 15 2024 15:46:53 %S A323988 1,2,5,10,23,46,102,204,443,886,1898,3796,8054,16108,33932,67864, %T A323988 142163,284326,592962,1185924,2464226,4928452,10209620,20419240, %U A323988 42190558,84381116,173962532,347925064,715908428,1431816856,2941192472,5882384944,12065310083,24130620166 %N A323988 a(n) = 2^(n - 1) + binomial(n, floor(n/2))*(n + 1)/2. %C A323988 This sequence was obtained by omitting the two initial zeros from A191386, which has a more complicated definition. The simple formula defining this sequence was found by Dan Velleman and _Stan Wagon_. See A191386 for further information, including references. %H A323988 Winston de Greef, <a href="/A323988/b323988.txt">Table of n, a(n) for n = 0..3300</a> %F A323988 G.f.: (1+s)/(2*s*(1-2*x)), where s = sqrt(1-4*x^2). %F A323988 a(0) = 1, a(1) = 2, a(2) = 5; thereafter (8*n+16)*a(n) + (-4*n-8)*a(n+1) + (-2*n-6)*a(n+2) + (n+3)*a(n+3) = 0. %t A323988 A323988[n_]:=2^(n-1)+Binomial[n,Floor[n/2]](n+1)/2;Array[A323988,50,0] (* _Paolo Xausa_, Nov 17 2023 *) %o A323988 (PARI) a(n) = 2^(n-1) + binomial(n, n\2)*(n+1)/2 \\ _Winston de Greef_, Sep 17 2023 %Y A323988 Cf. A191386. %K A323988 nonn %O A323988 0,2 %A A323988 _N. J. A. Sloane_, Feb 13 2019