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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 Table of n, a(n) for n=1..41. 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). 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 Adjacent sequences: A363703 A363704 A363705 * A363707 A363708 A363709 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.)