A217873 a(n) = 4*n*(n^2 + 2)/3.

0, 4, 16, 44, 96, 180, 304, 476, 704, 996, 1360, 1804, 2336, 2964, 3696, 4540, 5504, 6596, 7824, 9196, 10720, 12404, 14256, 16284, 18496, 20900, 23504, 26316, 29344, 32596, 36080, 39804, 43776, 48004, 52496, 57260, 62304, 67636, 73264, 79196, 85440, 92004

Offset: 0

Author

M. F. Hasler, Oct 13 2012

Keywords

• nonn
• easy

Comments

Occurs as 4th column in the table A142978 of figurate numbers for n-dimensional cross polytope.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A006527, A008412, A008590, A022144, A082138, A112087, A142978, A174794, A292022.

Programs

Magma

[4*n*(n^2+2)/3: n in [0..45]]; // Vincenzo Librandi, Nov 08 2012

Mathematica

Table[4n(n^2 + 2)/3, {n, 0, 39}] (* Alonso del Arte, Oct 22 2012 *)
LinearRecurrence[{4,-6,4,-1},{0,4,16,44},50] (* Harvey P. Dale, Mar 16 2015 *)

Maxima

makelist(4*n*(n^2+2)/3, n, 0, 41); /* Martin Ettl, Oct 15 2012 */

PARI

a(n)=(n^2+2)*n/3*4

Formula

a(n) = 4*A006527(n).

From Peter Luschny, Oct 14 2012: (Start)

a(n) = A008412(n)/2.

a(n) = A174794(n+1) - 1.

First differences are in A112087.

Second differences are in A008590 and A022144.

Binomial transformation of (a(n), n > 0) is A082138. (End)

G.f.: 4*x*(1 + x^2)/(x - 1)^4. - R. J. Mathar, Oct 15 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(0)=0, a(1)=4, a(2)=16, a(3)=44. - Harvey P. Dale, Mar 16 2015

From Elmo R. Oliveira, Aug 09 2025: (Start)

E.g.f.: 4*exp(x)*x*(3 + 3*x + x^2)/3.

a(n) = A292022(n)/3. (End)