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 A350413 #11 Dec 29 2021 17:53:09 %S A350413 0,0,0,0,1,6,24,79,233,640,1674,4224,10370,24912,58800,136767,314201, %T A350413 714209,1608604,3594007,7973108,17576844,38531060,84040238,182467033, %U A350413 394537387,849885436,1824495630,3904453264,8331493468,17730810536,37641301271,79727649682,168512283733 %N A350413 Total capacity of unrestricted compositions of n. %H A350413 Aubrey Blecher, Charlotte Brennan, and Arnold Knopfmacher, <a href="https://hosted.math.rochester.edu/ojac/vol13/161.pdf">The water capacity of integer compositions</a>, Online Journal of Analytic Combinatorics, Issue 13, 2018, #6. %o A350413 (PARI) v(z, N) = (-2 + 2*N + 5*z - 5*N*z - 4*z^2 + 3*N*z^2)/(-1 + 2*z)^2 + (1 - z)*(-3 + 4*z)/(1 - 2*z)*sum(r=2, N, 1/(1 - 2*z + z^r), O(z*z^N)) + sum(r=2, N, (1 - z)^2/(1 - 2*z + z^r)^2, O(z*z^N)); %o A350413 lista(nn) = Vec(v(z,nn), -nn); %Y A350413 Cf. A201126, A285766. %K A350413 nonn %O A350413 1,6 %A A350413 _Michel Marcus_, Dec 29 2021