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A211026 Number of segments needed to draw (on the infinite square grid) a diagram of regions and partitions of n. 3
4, 6, 8, 12, 16, 24, 32, 46, 62, 86, 114, 156, 204, 272, 354, 464, 596, 773, 982, 1256, 1586, 2006, 2512, 3152, 3918, 4874, 6022, 7438, 9132, 11210, 13686, 16700, 20288, 24622, 29768, 35956, 43276, 52032, 62372, 74678, 89168, 106350 (list; graph; refs; listen; history; text; internal format)
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

AUTHOR

Omar E. Pol, Oct 29 2012

STATUS

approved

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Last modified October 25 09:51 EDT 2021. Contains 348239 sequences. (Running on oeis4.)