A155965 a(n) = n*(n^2+4).

0, 5, 16, 39, 80, 145, 240, 371, 544, 765, 1040, 1375, 1776, 2249, 2800, 3435, 4160, 4981, 5904, 6935, 8080, 9345, 10736, 12259, 13920, 15725, 17680, 19791, 22064, 24505, 27120, 29915, 32896, 36069, 39440, 43015, 46800, 50801, 55024, 59475, 64160

Offset: 0

Author

Vincenzo Librandi, Jan 31 2009

Keywords

• nonn
• easy

Comments

The identity (n^3+4*n)^2 + (2*n^2+8)^2 = (n^2+4)^3 can be written as a(n)^2 + A155966(n)^2 = A087475(n)^3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A006003, A087475, A155966.

Programs

Mathematica

Table[n (n^2 + 4), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
CoefficientList[Series[x (5 - 4 x + 5 x^2)/(1 - x)^4, {x, 0, 60}], x] (* Vincenzo Librandi, May 03 2014 *)
LinearRecurrence[{4,-6,4,-1},{0,5,16,39},50] (* Harvey P. Dale, Jan 23 2019 *)

PARI

a(n)=n*(n^2+4) \\ Charles R Greathouse IV, Jan 11 2012

Sage

[lucas_number1(4,n,-2) for n in range(0, 41)] # Zerinvary Lajos, May 16 2009

Formula

G.f.: x*(5 - 4*x + 5*x^2)/(1 - x)^4. - Vincenzo Librandi, May 03 2014

a(n) = 4*a(n-1) - 6*a(n-2) +4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, May 03 2014

a(n) = A006003(n-1) + A006003(n+1). - Lechoslaw Ratajczak, Oct 31 2021