A304159 a(n) = 2*n^3 - 4*n^2 + 6*n - 2 (n>=1).
2, 10, 34, 86, 178, 322, 530, 814, 1186, 1658, 2242, 2950, 3794, 4786, 5938, 7262, 8770, 10474, 12386, 14518, 16882, 19490, 22354, 25486, 28898, 32602, 36610, 40934, 45586, 50578, 55922, 61630, 67714, 74186, 81058, 88342, 96050, 104194, 112786, 121838, 131362, 141370, 151874, 162886, 174418, 186482, 199090
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Emeric Deutsch and Sandi Klavžar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
- Eric Weisstein's World of Mathematics, Barbell Graph
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Maple
seq(2*n^3-4*n^2+6*n-2, n = 1 .. 40);
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Mathematica
Table[2n^3-4n^2+6n-2 ,{n,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{2,10,34,86},50] (* Harvey P. Dale, Mar 05 2023 *) -
PARI
Vec(2*x*(1 + x + 3*x^2 + x^3) / (1 - x)^4 + O(x^60)) \\ Colin Barker, May 09 2018
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PARI
a(n) = 2*n^3-4*n^2+6*n-2; \\ Altug Alkan, May 09 2018
Formula
a(n) = 2 * A100705(n-1).
From Colin Barker, May 09 2018: (Start)
G.f.: 2*x*(1 + x + 3*x^2 + x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. (End)
Comments