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A277981 a(n) = 4*n^2 + 18*n - 20. 1

%I #20 Sep 08 2022 08:46:17

%S -20,2,32,70,116,170,232,302,380,466,560,662,772,890,1016,1150,1292,

%T 1442,1600,1766,1940,2122,2312,2510,2716,2930,3152,3382,3620,3866,

%U 4120,4382,4652,4930,5216,5510,5812,6122,6440,6766,7100,7442,7792,8150

%N a(n) = 4*n^2 + 18*n - 20.

%C 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.

%C 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}.

%H E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

%H I. Gutman and K. C. Das, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match50/match50_83-92.pdf">The first Zagreb index 30 years after</a>, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.

%H J. Jeba Jesintha and K. Ezhilarasi Hilda, <a href="http://dx.doi.org/10.1007/s11786-015-0224-2">All uniform bow graphs are graceful</a>, Math. Comput. Sci., 9, 2015, 185-191.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F O.g.f.: 2*(17*x^2 - 31*x + 10)/(x - 1)^3.

%F E.g.f.: 2*(2*x^2 + 11*x - 10)*exp(x). - _Bruno Berselli_, Nov 11 2016

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Nov 11 2016

%p seq(4*n^2+18*n-20, n=0..40);

%t Table[4 n^2 + 18 n - 20, {n, 0, 50}] (* _Vincenzo Librandi_, Nov 11 2016 *)

%o (Sage) [4*n^2+18*n-20 for n in range(50)] # _Bruno Berselli_, Nov 11 2016

%o (Magma) [4*n^2+18*n-20: n in [0..50]]; // _Vincenzo Librandi_, Nov 11 2016

%o (PARI) a(n)=4*n^2+18*n-20 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A277982.

%K sign,easy

%O 0,1

%A _Emeric Deutsch_, Nov 10 2016

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)