A350413 - OEIS

%I #11 Dec 29 2021 17:53:09

%S 0,0,0,0,1,6,24,79,233,640,1674,4224,10370,24912,58800,136767,314201,

%T 714209,1608604,3594007,7973108,17576844,38531060,84040238,182467033,

%U 394537387,849885436,1824495630,3904453264,8331493468,17730810536,37641301271,79727649682,168512283733

%N Total capacity of unrestricted compositions of n.

%H 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 (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 lista(nn) = Vec(v(z,nn), -nn);

%Y Cf. A201126, A285766.

%K nonn

%O 1,6

%A _Michel Marcus_, Dec 29 2021