A211026 Number of segments needed to draw (on the infinite square grid) a diagram of regions and partitions of n.

4, 6, 8, 12, 16, 24, 32, 46, 62, 86, 114, 156, 204, 272, 354, 464, 596, 772, 982, 1256, 1586, 2006, 2512, 3152, 3918, 4874, 6022, 7438, 9132, 11210, 13686, 16700, 20288, 24622, 29768, 35956, 43276, 52032, 62372, 74678, 89168, 106350

Offset

1,1

Comments

On the infinite square grid the diagram of regions of the set of partitions of n is represented by a rectangle with base = n and height = A000041(n). The rectangle contains n shells. Each shell contains regions. Each row of a region is a part. Each part of size k contains k cells. The number of regions equals the number of partitions of n (see illustrations in the links section). For a minimalist version see A139582. For the definition of "region of n" see A206437.

Links

Table of n, a(n) for n=1..42.

Omar E. Pol, Illustration of initial terms of A211026 and of A066186

Omar E. Pol, Illustration of the seven regions of 5

Formula

a(n) = 2*A000041(n) + 2 = 2*A052810(n) = A139582(n) + 2.

Crossrefs

Cf. A000041, A052810, A135010, A139582, A141285, A186412, A186114, A187219, A193870, A194446, A194447, A206437, A211009

Sequence in context: A310663 A162294 A344994 * A090989 A161219 A310664

Adjacent sequences: A211023 A211024 A211025 * A211027 A211028 A211029

Keyword

nonn,changed

Author

Omar E. Pol, Oct 29 2012

Extensions

a(18) corrected by Georg Fischer, Apr 11 2024

Status

approved