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A277981 a(n) = 4*n^2 + 18*n - 20. 1
-20, 2, 32, 70, 116, 170, 232, 302, 380, 466, 560, 662, 772, 890, 1016, 1150, 1292, 1442, 1600, 1766, 1940, 2122, 2312, 2510, 2716, 2930, 3152, 3382, 3620, 3866, 4120, 4382, 4652, 4930, 5216, 5510, 5812, 6122, 6440, 6766, 7100, 7442, 7792, 8150 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..43.

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 xrange(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

Cf. A277982.

Sequence in context: A040398 A303847 A303849 * A040399 A040390 A040391

Adjacent sequences:  A277978 A277979 A277980 * A277982 A277983 A277984

KEYWORD

sign,easy

AUTHOR

Emeric Deutsch, Nov 10 2016

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)