

A304380


a(n) = 36*n^2  4*n (n>=1).


3



32, 136, 312, 560, 880, 1272, 1736, 2272, 2880, 3560, 4312, 5136, 6032, 7000, 8040, 9152, 10336, 11592, 12920, 14320, 15792, 17336, 18952, 20640, 22400, 24232, 26136, 28112, 30160, 32280, 34472, 36736, 39072, 41480, 43960, 46512, 49136, 51832, 54600, 57440
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OFFSET

1,1


COMMENTS

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.
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.
The Mpolynomial of O(n,n) is M(O(n,n);x,y) = 4*(n+1)x^2*y^2 + 8(n1)x^2 *y^3 + (6n^2  10n+4)x^3*y^3.
More generally, the Mpolynomial of O(m,n) is M(O(m,n); x,y) = 2(m+n+2)x^2*y^2+4(m+n2)x^2 *y^3+(6mn5m5n+4)x^3*y^3.
Sequence found by reading the line from 32, in the direction 32, 136, ..., in the square spiral whose vertices are the generalized 20gonal numbers.  Omar E. Pol, May 13 2018


LINKS



FORMULA

G.f.: 8*x*(4 + 5*x) / (1  x)^3.
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n>3.
(End)


MAPLE

seq(36*n^24*n, n = 1 .. 40);


PROG

(PARI) Vec(8*x*(4 + 5*x) / (1  x)^3 + O(x^40)) \\ Colin Barker, May 13 2018


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



