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%I #22 May 09 2020 07:22:31
%S 32,136,312,560,880,1272,1736,2272,2880,3560,4312,5136,6032,7000,8040,
%T 9152,10336,11592,12920,14320,15792,17336,18952,20640,22400,24232,
%U 26136,28112,30160,32280,34472,36736,39072,41480,43960,46512,49136,51832,54600,57440
%N a(n) = 36*n^2 - 4*n (n>=1).
%C a(n) is the first Zagreb index of the octagonal network O(n,n); O(m,n) is defined by Fig. 1 of the Siddiqui et al. reference.
%C The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
%C The M-polynomial of O(n,n) is M(O(n,n);x,y) = 4*(n+1)x^2*y^2 + 8(n-1)x^2 *y^3 + (6n^2 - 10n+4)x^3*y^3.
%C More generally, the M-polynomial of O(m,n) is M(O(m,n); x,y) = 2(m+n+2)x^2*y^2+4(m+n-2)x^2 *y^3+(6mn-5m-5n+4)x^3*y^3.
%C Sequence found by reading the line from 32, in the direction 32, 136, ..., in the square spiral whose vertices are the generalized 20-gonal numbers. - _Omar E. Pol_, May 13 2018
%H Colin Barker, <a href="/A304380/b304380.txt">Table of n, a(n) for n = 1..1000</a>
%H E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H M. K. Siddiqui, M. Naeem, N. A. Rahman, and M. Imran, <a href="https://joam.inoe.ro/articles/computing-topological-indices-of-certain-networks/">Computing topological indices of certain networks</a>, J. of Optoelectronics and Advanced Materials, 18, No. 9-10, 2016, 884-892.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Colin Barker_, May 13 2018: (Start)
%F G.f.: 8*x*(4 + 5*x) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F (End)
%p seq(36*n^2-4*n, n = 1 .. 40);
%o (PARI) Vec(8*x*(4 + 5*x) / (1 - x)^3 + O(x^40)) \\ _Colin Barker_, May 13 2018
%o (GAP) List([1..50],n->36*n^2-4*n); # _Muniru A Asiru_, May 13 2018
%Y Cf. A304381.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 13 2018
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