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%I #53 Sep 01 2023 04:21:02
%S 9,36,99,216,405,684,1071,1584,2241,3060,4059,5256,6669,8316,10215,
%T 12384,14841,17604,20691,24120,27909,32076,36639,41616,47025,52884,
%U 59211,66024,73341,81180,89559,98496,108009,118116,128835,140184
%N a(n) = n^3 + (n+1)^3 + (n+2)^3.
%C a(3) = 216 = 6^3 (a cube). - Howard Berman (howard_berman(AT)hotmail.com), Nov 07 2008
%C Pairs [n,a(n)] for n<=10^7 such that a(n) is a perfect power are [0, 9], [1, 36], [3, 216], [23, 41616]. - _Joerg Arndt_, Jan 25 2011
%C Sums of three consecutive cubes. - Al Hakanson (hawkuu(AT)gmail.com), May 20 2009
%H Vincenzo Librandi, <a href="/A027602/b027602.txt">Table of n, a(n) for n = 0..750</a>
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/sumcube.htm">Palindromic Sums of Cubes of Consecutive Integers</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 1*a(n-4) for n>=4.
%F a(n) = 9*A006527(n+1). - _Lekraj Beedassy_, Feb 01 2007
%F a(n) = 3*n^3 + 9*n^2 + 15*n + 9.
%F G.f.: 9*(1+x^2)/(1-x)^4. - _Bruno Berselli_, Jan 21 2011
%F a(n) = A008585(n+1)*A059100(n+1). - _Bruno Berselli_, Jan 21 2011
%F E.g.f.: 3*(3 + 9*x + 6*x^2 + x^3)*exp(x). - _G. C. Greubel_, Aug 24 2022
%F Sum_{n>=0} 1/a(n) = (2*gamma + polygamma(0, 1-i*sqrt(2)) + polygamma(0, 1+i*sqrt(2))/12 = 0.161383557127191633050394086192620963436504... where i denotes the imaginary unit. - _Stefano Spezia_, Aug 31 2023
%t f[n_]:=n^3; Table[f[n]+f[n+1]+f[n+2], {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009 *)
%o (Sage) [i^3+(i+1)^3+(i+2)^3 for i in range(0,48)] # _Zerinvary Lajos_, Jul 03 2008
%o (Magma) [3*n^3 + 9*n^2 + 15*n + 9: n in [0..60]]; // _Vincenzo Librandi_, Apr 26 2011
%o (PARI) a(n)=3*(n^3 + 3*n^2 + 5*n + 3) \\ _Charles R Greathouse IV_, Jun 11 2015
%o (Python)
%o A027602_list, m = [], [18, 0, 9, 9]
%o for _ in range(10**2):
%o A027602_list.append(m[-1])
%o for i in range(3):
%o m[i+1] += m[i] # _Chai Wah Wu_, Dec 15 2015
%Y Cf. A000537, A003215, A006527, A008585, A059100.
%Y Cf. A000578, A005898, A027603, A027604.
%K nonn,easy
%O 0,1
%A _Patrick De Geest_
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