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

1,2

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

Table of n, a(n) for n=1..20.

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

Prog

(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

Crossrefs

Cf. A001003, A192933.

Sequence in context: A154627 A320350 A354495 * A091172 A091168 A126596

Adjacent sequences: A336280 A336281 A336282 * A336284 A336285 A336286

Keyword

nonn

Author

Petros Hadjicostas, Jul 15 2020

Status

approved