A363706 a(n) is the sigma irregularity of the n-th power of a path graph of length at least 3*n.

2, 14, 52, 140, 310, 602, 1064, 1752, 2730, 4070, 5852, 8164, 11102, 14770, 19280, 24752, 31314, 39102, 48260, 58940, 71302, 85514, 101752, 120200, 141050, 164502, 190764, 220052, 252590, 288610, 328352, 372064, 420002, 472430, 529620, 591852, 659414, 732602, 811720, 897080, 989002

Offset: 1

Author

Allan Bickle, Jun 16 2023

Keywords

• nonn
• easy

Comments

The sigma irregularity of a graph is the sum of the squares of the differences between the degrees over all edges of the graph.

Examples

			A path of length at least 3 has two edges between vertices with degrees 1 and 2. Thus a(1) = 2.
		

Links

• Allan Bickle and Zhongyuan Che, Irregularities of Maximal k-degenerate Graphs, Discrete Applied Math. 331 (2023) 70-87.
• Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A006325.

Cf. A011379, A181617, A270205 (sigma irregularities of maximal k-degenerate graphs).

Programs

Mathematica

Table[(n^4 + 2*n^3 + 2*n^2 + n)/3, {n, 1, 40}] (* Amiram Eldar, Jul 28 2023 *)

Formula

a(n) = (n^4 + 2*n^3 + 2*n^2 + n)/3.

a(n) = 2*A006325(n+1).

G.f.: 2*x*(1 + x)^2/(1 - x)^5. - Stefano Spezia, Jul 28 2023