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A016959
a(n) = (6*n + 4)^3.
14
64, 1000, 4096, 10648, 21952, 39304, 64000, 97336, 140608, 195112, 262144, 343000, 438976, 551368, 681472, 830584, 1000000, 1191016, 1404928, 1643032, 1906624, 2197000, 2515456, 2863288, 3241792
OFFSET
0,1
FORMULA
G.f.: 8*(x^3 + 60*x^2 + 93*x + 8)/(1-x)^4. - Vincenzo Librandi, Jan 27 2013
Sum_{n>=0} 1/a(n) = -Pi^3 / (324*sqrt(3)) + 13*zeta(3)/216. - Amiram Eldar, Oct 02 2020
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 02 2020
EXAMPLE
a(0) = (6*0 + 4)^3 = 4^3 = 64.
MATHEMATICA
CoefficientList[Series[8*(x^3 + 60*x^2 + 93*x + 8)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)
(6*Range[0, 30]+4)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {64, 1000, 4096, 10648}, 30] (* Harvey P. Dale, Nov 22 2018 *)
PROG
(Magma) [(6*n+4)^3: n in [0..40]]; // Vincenzo Librandi, May 06 2011
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved