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%I #21 Feb 19 2024 01:35:43
%S 2,14,52,140,310,602,1064,1752,2730,4070,5852,8164,11102,14770,19280,
%T 24752,31314,39102,48260,58940,71302,85514,101752,120200,141050,
%U 164502,190764,220052,252590,288610,328352,372064,420002,472430,529620,591852,659414,732602,811720,897080,989002
%N a(n) is the sigma irregularity of the n-th power of a path graph of length at least 3*n.
%C The sigma irregularity of a graph is the sum of the squares of the differences between the degrees over all edges of the graph.
%H Allan Bickle and Zhongyuan Che, <a href="https://doi.org/10.1016/j.dam.2023.01.020">Irregularities of Maximal k-degenerate Graphs</a>, Discrete Applied Math. 331 (2023) 70-87.
%H Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (n^4 + 2*n^3 + 2*n^2 + n)/3.
%F a(n) = 2*A006325(n+1).
%F G.f.: 2*x*(1 + x)^2/(1 - x)^5. - _Stefano Spezia_, Jul 28 2023
%e A path of length at least 3 has two edges between vertices with degrees 1 and 2. Thus a(1) = 2.
%t Table[(n^4 + 2*n^3 + 2*n^2 + n)/3, {n, 1, 40}] (* _Amiram Eldar_, Jul 28 2023 *)
%Y Cf. A006325.
%Y Cf. A011379, A181617, A270205 (sigma irregularities of maximal k-degenerate graphs).
%K nonn,easy
%O 1,1
%A _Allan Bickle_, Jun 16 2023
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