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

100, 225, 440, 775, 1260, 1925, 2800, 3915, 5300, 6985, 9000, 11375, 14140, 17325, 20960, 25075, 29700, 34865, 40600, 46935, 53900, 61525, 69840, 78875, 88660, 99225, 110600, 122815, 135900, 149885, 164800, 180675, 197540

Offset: 0

Author

Patrick De Geest

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Patrick De Geest, Palindromic Sums of Cubes of Consecutive Integers
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000578, A005898, A027602, A027603.

Cf. A008587, A114949.

Programs

Magma

[5*n^3+30*n^2+90*n+100: n in [0..40]]; // Vincenzo Librandi, Jun 04 2011

Mathematica

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 *)
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 *)
Total/@Partition[Range[0,40]^3,5,1] (* Harvey P. Dale, Mar 28 2025 *)

PARI

a(n)=5*((n+6)*n+18)*n+100 \\ Charles R Greathouse IV, Jun 28 2011

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

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 1*a(n-4) for n >= 4.

From Bruno Berselli, Jan 24 2011: (Start)

G.f.: 5*(20 - 35*x + 28*x^2 - 7*x^3)/(1-x)^4.

a(n) = 5*n^3 + 30*n^2 + 90*n + 100 = A008587(n+2)*A114949(n+2). (End)

E.g.f.: 5*(4+x)*(5+5*x+x^2)*exp(x). - G. C. Greubel, Aug 24 2022