OFFSET
0,2
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).
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.
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(0)=0, a(1)=4, a(2)=16, a(3)=44, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Mar 16 2015
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 *)
PROG
(PARI) a(n)=(n^2+2)*n/3*4
(Maxima) makelist(4*n*(n^2+2)/3, n, 0, 41); /* Martin Ettl, Oct 15 2012 */
(Magma) [4*n*(n^2+2)/3: n in [0..45]]; // Vincenzo Librandi, Nov 08 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Oct 13 2012
STATUS
approved