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A304381
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a(n) = 54*n^2 - 26*n + 4 (n>=1).
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2
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32, 168, 412, 764, 1224, 1792, 2468, 3252, 4144, 5144, 6252, 7468, 8792, 10224, 11764, 13412, 15168, 17032, 19004, 21084, 23272, 25568, 27972, 30484, 33104, 35832, 38668, 41612, 44664, 47824, 51092, 54468, 57952, 61544, 65244, 69052, 72968, 76992, 81124, 85364
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OFFSET
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1,1
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COMMENTS
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a(n) is the second Zagreb index of the octagonal network O(n,n); O(m,n) is defined by Fig. 1 of the Siddiqui et al. reference.
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.
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.
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.
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LINKS
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FORMULA
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G.f.: 4*x*(8 + 18*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
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MAPLE
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seq(54*n^2-26*n+4, n = 1 .. 40);
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MATHEMATICA
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Table[54n^2-26n+4, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {32, 168, 412}, 40] (* Harvey P. Dale, Mar 21 2020 *)
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PROG
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(PARI) Vec(4*x*(8 + 18*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 13 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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