A136038 a(n) = n^6 - n^4.

0, 0, 48, 648, 3840, 15000, 45360, 115248, 258048, 524880, 990000, 1756920, 2965248, 4798248, 7491120, 11340000, 16711680, 24054048, 33907248, 46915560, 63840000, 85571640, 113145648, 147756048, 190771200, 243750000, 308458800, 386889048, 481275648

Offset: 0

Author

Rolf Pleisch, Mar 16 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A013661, A013662, A072691, A267315.

Programs

Magma

[n^6-n^4: n in [0..30]]; // Vincenzo Librandi, Feb 20 2012

Maple

map(n -> n^6 - n^4, [$0..100]); # Robert Israel, Aug 28 2018

Mathematica

a[n_]:=n^6-n^4; a[Range[0,60]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,48,648,3840,15000,45360},30] (* Harvey P. Dale, May 17 2018 *)

Formula

From R. J. Mathar, Feb 06 2010: (Start)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: 24*x^2*(1+x)*(2*x^2+11*x+2)/(1-x)^7. (End)

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=2} 1/a(n) = 11/4 - Pi^2/6 - Pi^4/90 = 11/4 - A013661 - A013662.

Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/720 + Pi^2/12 - 7/4 = A267315 + A072691 - 7/4. (End)