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A027604 a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3 + (n+4)^3.

%I A027604 #37 Mar 28 2025 15:33:01
%S A027604 100,225,440,775,1260,1925,2800,3915,5300,6985,9000,11375,14140,17325,
%T A027604 20960,25075,29700,34865,40600,46935,53900,61525,69840,78875,88660,
%U A027604 99225,110600,122815,135900,149885,164800,180675,197540
%N A027604 a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3 + (n+4)^3.
%H A027604 Vincenzo Librandi, <a href="/A027604/b027604.txt">Table of n, a(n) for n = 0..1000</a>
%H A027604 Patrick De Geest, <a href="http://www.worldofnumbers.com/sumcube.htm">Palindromic Sums of Cubes of Consecutive Integers</a>
%H A027604 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A027604 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 1*a(n-4) for n >= 4.
%F A027604 From _Bruno Berselli_, Jan 24 2011: (Start)
%F A027604 G.f.: 5*(20 - 35*x + 28*x^2 - 7*x^3)/(1-x)^4.
%F A027604 a(n) = 5*n^3 + 30*n^2 + 90*n + 100 = A008587(n+2)*A114949(n+2). (End)
%F A027604 E.g.f.: 5*(4+x)*(5+5*x+x^2)*exp(x). - _G. C. Greubel_, Aug 24 2022
%t A027604 Table[n^3 +(n+1)^3 +(n+2)^3 +(n+3)^3 +(n+4)^3, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)
%t A027604 Table[100+90n+30n^2+5n^3,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{100,225,440,775},40] (* _Harvey P. Dale_, Dec 19 2022 *)
%t A027604 Total/@Partition[Range[0,40]^3,5,1] (* _Harvey P. Dale_, Mar 28 2025 *)
%o A027604 (Sage) [n^3+(n+1)^3+(n+2)^3+(n+3)^3+(n+4)^3 for n in range(0,35)] # _Zerinvary Lajos_, Jul 03 2008
%o A027604 (Magma) [5*n^3+30*n^2+90*n+100: n in [0..40]]; // _Vincenzo Librandi_, Jun 04 2011
%o A027604 (PARI) a(n)=5*((n+6)*n+18)*n+100 \\ _Charles R Greathouse IV_, Jun 28 2011
%Y A027604 Cf. A000578, A005898, A027602, A027603.
%Y A027604 Cf. A008587, A114949.
%K A027604 nonn,easy
%O A027604 0,1
%A A027604 _Patrick De Geest_