A139582 Twice partition numbers.

2, 2, 4, 6, 10, 14, 22, 30, 44, 60, 84, 112, 154, 202, 270, 352, 462, 594, 770, 980, 1254, 1584, 2004, 2510, 3150, 3916, 4872, 6020, 7436, 9130, 11208, 13684, 16698, 20286, 24620, 29766, 35954, 43274, 52030, 62370, 74676, 89166, 106348, 126522, 150350, 178268, 211116, 249508, 294546, 347050, 408452

Offset

0,1

Comments

Except for the first term the number of segments needed to draw (on the infinite square grid) a minimalist diagram of regions and partitions of n. Therefore A000041(n) is also the number of pairs of orthogonal segments (L-shaped) in the same diagram (See links section). For the definition of "regions of n" see A206437. - Omar E. Pol, Oct 29 2012

Links

Table of n, a(n) for n=0..50.

V. Modrak, D. Marton, A framework for generating and complexity assessment of assembly supply chains, in Nonlinear Science and Complexity (NSC), 2012 IEEE 4th International Conference on, Date of Conference: 6-11 Aug. 2012; Digital Object Identifier: 10.1109/NSC.2012.6304712. - From N. J. A. Sloane, Dec 27 2012

V. Modrak, D. Marton, Development of Metrics and a Complexity Scale for the Topology of Assembly Supply Chains, Entropy 2013, 15, 4285-4299; doi:10.3390/e15104285.

V. Modrak, D. Marton, Approaches to Defining and Measuring Assembly Supply Chain Complexity, Discontinuity and Complexity in Nonlinear Physical Systems, Vol. 6, 2014, pp. 192-213.

V. Modrak, D. Marton, Configuration complexity assessment of convergent supply chain systems, International Journal of General Systems, Volume 43, Issue 5, 2014.

Omar E. Pol, Illustration of initial terms of A139582 (n>=1) and of A066186

Formula

a(n) = 2*A000041(n).

Example

The number of partitions of 6 is 11, then a(6) = 2*11 = 22.

Mathematica

Array[2 PartitionsP@# &, 50, 0] (* Robert G. Wilson v, Feb 11 2018 *)

Prog

(PARI) a(n) = 2*numbpart(n); \\ Michel Marcus, Feb 12 2018

Crossrefs

Cf. A000041, A135010, A206437, A211026.

Sequence in context: A083848 A330644 A278297 * A300415 A355908 A306731

Adjacent sequences: A139579 A139580 A139581 * A139583 A139584 A139585

Keyword

easy,nonn

Author

Omar E. Pol, May 14 2008

Extensions

More terms from Omar E. Pol, Feb 11 2018

Status

approved