A336283 - OEIS

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

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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