This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016779 #67 Dec 29 2024 21:01:45
%S A016779 1,64,343,1000,2197,4096,6859,10648,15625,21952,29791,39304,50653,
%T A016779 64000,79507,97336,117649,140608,166375,195112,226981,262144,300763,
%U A016779 343000,389017,438976,493039,551368,614125,681472,753571,830584,912673,1000000,1092727,1191016
%N A016779 a(n) = (3*n + 1)^3.
%C A016779 The inverse binomial transform is 1, 63, 216, 162, 0, 0, 0 (0 continued). _R. J. Mathar_, May 07 2008
%C A016779 Perfect cubes with digital root 1 in base 10. Proof: perfect cubes are one of (3*s)^3, (3*s+1)^3 or (3*s+2)^3. Digital roots of (3*s)^3 are 0, digital roots of (3*s+1)^3 are 1, and digital roots of (3*s+2)^3 are 8, using trinomial expansion and the multiplicative property of digits roots. - _R. J. Mathar_, Jul 31 2010
%D A016779 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
%D A016779 Amarnath Murthy, Fabricating a perfect cube with a given valid digit sum (to be published)
%H A016779 Harry J. Smith, <a href="/A016779/b016779.txt">Table of n, a(n) for n = 0..1000</a>
%H A016779 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A016779 Sum_{n>=0} 1/a(n) = 2*Pi^3 / (81*sqrt(3)) + 13*zeta(3)/27.
%F A016779 O.g.f.: (1 + 60*x + 93*x^2 + 8*x^3)/(1 - x)^4. - _R. J. Mathar_, May 07 2008
%F A016779 E.g.f.: (1 + 63*x + 108*x^2 + 27*x^3)*exp(x). - _Ilya Gutkovskiy_, Jun 16 2016
%F A016779 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Oct 02 2020
%F A016779 Sum_{n>=1} (-1)^n/a(n) = A226735. - _R. J. Mathar_, Feb 07 2024
%e A016779 a(2) = (3*2+1)^3 = 343.
%e A016779 a(6) = (3*6+1)^3 = 6859.
%t A016779 Table[(3n+1)^3,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)
%t A016779 LinearRecurrence[{4,-6,4,-1},{1,64,343,1000},40] (* _Harvey P. Dale_, Oct 31 2016 *)
%o A016779 (Magma) [(3*n+1)^3: n in [0..30]]; // _Vincenzo Librandi_, May 09 2011
%o A016779 (PARI) a(n)=(3*n+1)^3 \\ _Charles R Greathouse IV_, Jan 02 2012
%Y A016779 Cf. A016791, A054966, A226735.
%K A016779 nonn,easy
%O A016779 0,2
%A A016779 _N. J. A. Sloane_