

A161712


a(n) = (4*n^3  6*n^2 + 8*n + 3)/3.


17



1, 3, 9, 27, 65, 131, 233, 379, 577, 835, 1161, 1563, 2049, 2627, 3305, 4091, 4993, 6019, 7177, 8475, 9921, 11523, 13289, 15227, 17345, 19651, 22153, 24859, 27777, 30915, 34281, 37883, 41729, 45827, 50185, 54811, 59713, 64899, 70377, 76155
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OFFSET

0,2


COMMENTS

{a(k): 0 <= k < 4} = divisors of 27:
a(n) = A027750(A006218(26) + k + 1), 0 <= k < A000005(27).
a(n), n > 0 is the number of points of the halfinteger 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(5x2)))/(x1)^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^36n^2+8n+3)/3, {n, 0, 80}] (* Harvey P. Dale, Apr 13 2011 *)


PROG

(PARI) a(n)=(4*n^36*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

Sequence in context: A201202 A260938 A274626 * A280466 A137368 A191007
Adjacent sequences: A161709 A161710 A161711 * A161713 A161714 A161715


KEYWORD

nonn,easy


AUTHOR

Reinhard Zumkeller, Jun 17 2009


STATUS

approved



