OFFSET
0,1
COMMENTS
For n>=3, a(n) is the first Zagreb index of the uniform bow graph B[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. The uniform bow graph B[n] consists of two path graphs P[n] and an additional vertex joined by 2n edges to the vertices of the paths.
The M-polynomial of the uniform bow graph B[n] is M(B[n],x,y) = 4*x^2*y^3 + 4*x^2*y^{2*n} + (2*n-6)*x^3*y^3 + (2*n-4)*x^3*y^{2*n}.
LINKS
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
J. Jeba Jesintha and K. Ezhilarasi Hilda, All uniform bow graphs are graceful, Math. Comput. Sci., 9, 2015, 185-191.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
O.g.f.: 2*(17*x^2 - 31*x + 10)/(x - 1)^3.
E.g.f.: 2*(2*x^2 + 11*x - 10)*exp(x). - Bruno Berselli, Nov 11 2016
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Nov 11 2016
MAPLE
seq(4*n^2+18*n-20, n=0..40);
MATHEMATICA
Table[4 n^2 + 18 n - 20, {n, 0, 50}] (* Vincenzo Librandi, Nov 11 2016 *)
PROG
(Sage) [4*n^2+18*n-20 for n in range(50)] # Bruno Berselli, Nov 11 2016
(Magma) [4*n^2+18*n-20: n in [0..50]]; // Vincenzo Librandi, Nov 11 2016
(PARI) a(n)=4*n^2+18*n-20 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Emeric Deutsch, Nov 10 2016
STATUS
approved