A304833 a(n) = 3*n^2 + 38*n - 76 (n>=2).

12, 65, 124, 189, 260, 337, 420, 509, 604, 705, 812, 925, 1044, 1169, 1300, 1437, 1580, 1729, 1884, 2045, 2212, 2385, 2564, 2749, 2940, 3137, 3340, 3549, 3764, 3985, 4212, 4445, 4684, 4929, 5180, 5437, 5700, 5969, 6244, 6525, 6812, 7105, 7404, 7709, 8020, 8337, 8660, 8989, 9324, 9665, 10012, 10365, 10724, 11089

Offset

2,1

Comments

For n>=3, a(n) is the second Zagreb index of the Mycielskian of the path graph P[n]. For the Mycielskian, see p. 205 of the West reference and/or the Wikipedia link.

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.

For n>=3 the M-polynomial of the considered Mycielskian is 2*x^2*y^3 + 4*x^2*y^4 + 2*x^2*y^n + 2*(n-3)*x^3*y^4 + (n-2)*x^3*y^n +(n-3)*x^4*y^4.

References

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

Wikipedia, Mycielskian

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, May 21 2018: (Start)

G.f.: x^2*(12 + 29*x - 35*x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Maple

seq(3*n^2+38*n-76, n = 2 .. 55);

Prog

(PARI) a(n) = 3*n^2 + 38*n - 76 \\ Felix Fröhlich, May 20 2018
(PARI) Vec(x^2*(12 + 29*x - 35*x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 21 2018
(GAP) List([2..60], n->3*n^2+38*n-76); # Muniru A Asiru, May 20 2018

Crossrefs

Cf. A304832.

Sequence in context: A104062 A232383 A003868 * A363591 A223234 A289223

Adjacent sequences: A304830 A304831 A304832 * A304834 A304835 A304836

Keyword

nonn,easy

Author

Emeric Deutsch, May 20 2018

Status

approved