A336283 - OEIS

%I #10 Jul 16 2020 11:48:29

%S 1,3,20,152,1264,11168,102976,979840,9550592,94876160,957101056,

%T 9778354176,100970557440,1052097552384,11048512143360,116814955118592,

%U 1242454765535232,13284730164346880,142713773337346048,1539605733158944768

%N Row sums of A192933.

%C a(n) is the total number of bimonotone subdivisions of a 2-row grid with n points on the top row and k points at the bottom row for k from 1 to n. See Robeva and Sun (2020) for more details. (The authors do not seem to care about the value of a(1) because they do not consider subdivisions of a degenerate polygon with only one side.)

%H Elina Robeva and Melinda Sun, <a href="https://arxiv.org/abs/2007.00877">Bimonotone Subdivisions of Point Configurations in the Plane</a>, arXiv:2007.00877 [math.CO], 2020.

%F O.g.f.: x*(1-x)*(2*g(2*x) - 1), where g(x) is the o.g.f. of A001003.

%F a(n) = 2^n*A001003(n-1) - 2^(n-1)*A001003(n-2) for n >= 3.

%o (PARI) lista(nn) = {my(T=matrix(nn, nn)); T[1, 1] = 1; for (n=2, nn, for (k=1, n, T[n, k] = sum(i=1, n, sum(j=1, k, if ((i!=n) || (j!=k), T[i, j]))); ); ); vector(nn, k, vecsum(vector(k, i, T[k, i]))); } \\ _Michel Marcus_, Jul 16 2020

%Y Cf. A001003, A192933.

%K nonn

%O 1,2

%A _Petros Hadjicostas_, Jul 15 2020