A336283 Row sums of A192933.

1, 3, 20, 152, 1264, 11168, 102976, 979840, 9550592, 94876160, 957101056, 9778354176, 100970557440, 1052097552384, 11048512143360, 116814955118592, 1242454765535232, 13284730164346880, 142713773337346048, 1539605733158944768

Offset: 1

Author

Petros Hadjicostas, Jul 15 2020

Keywords

• nonn

Comments

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.)

Links

• Elina Robeva and Melinda Sun, Bimonotone Subdivisions of Point Configurations in the Plane, arXiv:2007.00877 [math.CO], 2020.

Crossrefs

Cf. A001003, A192933.

Programs

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

Formula

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

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