A197986 a(n) = round((n+1/n)^3).
8, 16, 37, 77, 141, 235, 364, 536, 756, 1030, 1364, 1764, 2236, 2786, 3420, 4144, 4964, 5886, 6916, 8060, 9324, 10714, 12236, 13896, 15700, 17654, 19764, 22036, 24476, 27090, 29884, 32864, 36036, 39406, 42980, 46764, 50764
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[Round((n+1/n)^3): n in [1..60]]
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Mathematica
Table[Round[(n+1/n)^3],{n,40}] (* or *) Join[{8,16,37,77,141,235}, LinearRecurrence[ {4,-6,4,-1},{364,536,756,1030},40]] (* Harvey P. Dale, Apr 05 2012 *) -
SageMath
[8,16,37,77,141,235]+[n*(n^2+3) for n in range(7,51)] # G. C. Greubel, Feb 04 2024
Formula
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(1)= 8, a{2}=16, a(3)=37, a(4)=77, a(5)=141, a(6)=235, a(7)=364, a(8)=536, a(9)=756, a(10)=1030. - Harvey P. Dale, Apr 05 2012
From G. C. Greubel, Feb 04 2024: (Start)
a(n) = n*(n^2+3) for n > 6, with a(1)=8, a(2)=16, a(3)=37, a(4)=77, a(5)=141, a(6)=235.
G.f.: x*(8 - 16*x + 21*x^2 - 7*x^3 - x^4 + x^5 - x^6 + 3*x^7 - 3*x^8 + x^9)/(1-x)^4.
E.g.f.: 4*x + x^2 + x^3/3! + x^4/4! + x^5/5! + x^6/6! + x*(4 + 3*x + x^2)*exp(x). (End)