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

Author

Omar E. Pol, Oct 29 2012

Keywords

• nonn

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

• Omar E. Pol, Illustration of initial terms of A211026 and of A066186
• Omar E. Pol, Illustration of the seven regions of 5

Crossrefs

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

Formula

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

Extensions

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