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A363706 a(n) is the sigma irregularity of the n-th power of a path graph of length at least 3*n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
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.
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
EXAMPLE
A path of length at least 3 has two edges between vertices with degrees 1 and 2. Thus a(1) = 2.
MATHEMATICA
Table[(n^4 + 2*n^3 + 2*n^2 + n)/3, {n, 1, 40}] (* Amiram Eldar, Jul 28 2023 *)
CROSSREFS
Cf. A006325.
Cf. A011379, A181617, A270205 (sigma irregularities of maximal k-degenerate graphs).
Sequence in context: A143553 A341493 A064363 * A259125 A067056 A208428
KEYWORD
nonn,easy
AUTHOR
Allan Bickle, Jun 16 2023
STATUS
approved

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Last modified July 22 08:19 EDT 2024. Contains 374485 sequences. (Running on oeis4.)