OFFSET
1,1
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).
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)
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 *)
PROG
(Magma) [Round((n+1/n)^3): n in [1..60]]
(SageMath) [8, 16, 37, 77, 141, 235]+[n*(n^2+3) for n in range(7, 51)] # G. C. Greubel, Feb 04 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 21 2011
STATUS
approved