A017331 a(n) = (10*n + 5)^3.
125, 3375, 15625, 42875, 91125, 166375, 274625, 421875, 614125, 857375, 1157625, 1520875, 1953125, 2460375, 3048625, 3723875, 4492125, 5359375, 6331625, 7414875, 8615125, 9938375, 11390625, 12977875, 14706125, 16581375, 18609625, 20796875, 23149125, 25672375
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(10*n+5)^3: n in [0..35]]; // Vincenzo Librandi, Aug 02 2011
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Mathematica
Table[(10*n + 5)^3, {n, 0, 30}] (* Amiram Eldar, Apr 18 2023 *) LinearRecurrence[{4,-6,4,-1},{125,3375,15625,42875},30] (* Harvey P. Dale, Aug 23 2024 *) -
PARI
a(n)=(10*n+5)^3 \\ Charles R Greathouse IV, Aug 02 2011
Formula
G.f.: 125*(x+1)*(x^2 + 22*x + 1)/(x-1)^4. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^3.
a(n) = 5^3 * A016755(n).
Sum_{n>=0} 1/a(n) = 7*zeta(3)/1000.
Sum_{n>=0} (-1)^n/a(n) = Pi^3/4000. (End)