OFFSET
0,2
COMMENTS
{a(k): 0 <= k < 4} = divisors of 27:
a(n), n > 0 is the number of points of the half-integer lattice in R^n that lie in the open unit ball. - Tom Harris, Jun 15 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Reinhard Zumkeller, Enumerations of Divisors
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = C(n,0) + 2*C(n,1) + 4*C(n,2) + 8*C(n,3).
G.f.: ((x+1)(1+x(5x-2)))/(x-1)^4. - Harvey P. Dale, Apr 13 2011
E.g.f.: (1/3)*(4*x^3 + 6*x^2 + 6*x + 3)*exp(x). - G. C. Greubel, Jul 16 2017
EXAMPLE
Differences of divisors of 27 to compute the coefficients of their interpolating polynomial, see formula:
1 3 9 27
2 6 18
4 12
8
MATHEMATICA
Table[(4n^3-6n^2+8n+3)/3, {n, 0, 80}] (* Harvey P. Dale, Apr 13 2011 *)
PROG
(PARI) a(n)=(4*n^3-6*n^2+8*n)/3+1 \\ Charles R Greathouse IV, Jul 16 2011
(Magma) [(4*n^3 - 6*n^2 + 8*n + 3)/3: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jun 17 2009
STATUS
approved