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%I #20 Mar 13 2022 14:00:18
%S 8,40,72,104,136,168,200,232,264,296,328,360,392,424,456,488,520,552,
%T 584,616,648,680,712,744,776,808,840,872,904,936,968,1000,1032,1064,
%U 1096,1128,1160,1192,1224,1256,1288,1320,1352,1384,1416,1448,1480,1512,1544,1576
%N a(n) = 32*n - 24 (n>=1).
%C a(n) (n>=2) is the second Zagreb index of the single oxide chain SOX(n), defined pictorially in the Simonraj et al. reference (Fig. 4, where SOX(9) is shown marked as OX(1,9)).
%C The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C The M-polynomial of SL(n) is M(SL(n);x,y) = 2*x^2*y^2 + 2*n*x^2*y^4 + (n - 2)*x^4*y^4 (n>=2).
%H Muniru A Asiru, <a href="/A305075/b305075.txt">Table of n, a(n) for n = 1..5000</a>
%H F. Simonraj and A. George, <a href="http://doi.org/10.7763/IJFCC.2013.V2.128">Topological properties of few poly oxide, poly silicate, DOX and DSL networks</a>, International J. of Future Computer and Communication, 2, No. 2, 2013, 90-95.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1)
%F a(n) = A063164(n) for n > 1.
%F From _Colin Barker_, May 29 2018: (Start)
%F G.f.: 8*x*(1 + 3*x) / (1 - x)^2.
%F a(n) = 2*a(n-1) - a(n-2) for n>2.
%F (End)
%p seq(32*n - 24, n = 1 .. 50);
%t 32*Range[60]-24 (* or *) LinearRecurrence[{2,-1},{8,40},60] (* _Harvey P. Dale_, Mar 13 2022 *)
%o (GAP) List([1..50], n->32*n-24); # _Muniru A Asiru_, May 27 2018
%o (PARI) Vec(8*x*(1 + 3*x) / (1 - x)^2 + O(x^50)) \\ _Colin Barker_, May 29 2018
%Y Cf. A063164, A305074.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 26 2018
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