A304508 a(n) = 5*(3*n+1)*(9*n+8)/2 (n>=0).
20, 170, 455, 875, 1430, 2120, 2945, 3905, 5000, 6230, 7595, 9095, 10730, 12500, 14405, 16445, 18620, 20930, 23375, 25955, 28670, 31520, 34505, 37625, 40880, 44270, 47795, 51455, 55250, 59180, 63245, 67445, 71780, 76250, 80855, 85595, 90470, 95480, 100625, 105905, 111320
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Emeric Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, Vol. 6, No. 2, 2015, pp. 93-102.
- T. Doslic and M. Saheli, Augmented eccentric connectivity index of single-defect nanocones, J. of Mathematical Nanoscience, Vol. 1, No. 1, 2011, pp. 25-31.
- A. Khaksar, M. Ghorbani, and H. R. Maimani, On atom bond connectivity and GA indices of nanocones, Optoelectronics and Advanced Materials - Rapid Communications, Vol. 4, No. 11, 2010, pp. 1868-1870.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Maple
seq((1/2)*(5*(3*n+1))*(9*n+8), n = 0 .. 40);
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Mathematica
Array[5 (3 # + 1) (9 # + 8)/2 &, 41, 0] (* or *) LinearRecurrence[{3, -3, 1}, {20, 170, 455}, 41] (* or *) CoefficientList[Series[5 (4 + 22 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, May 14 2018 *) -
PARI
a(n) = 5*(3*n+1)*(9*n+8)/2; \\ Altug Alkan, May 14 2018
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PARI
Vec(5*(4 + 22*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 14 2018
Formula
From Colin Barker, May 14 2018: (Start)
G.f.: 5*(4 + 22*x + x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
From Elmo R. Oliveira, Nov 15 2024: (Start)
E.g.f.: 5*exp(x)*(8 + 60*x + 27*x^2)/2.
Comments