|
|
A161707
|
|
a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3.
|
|
18
|
|
|
1, 3, 7, 21, 53, 111, 203, 337, 521, 763, 1071, 1453, 1917, 2471, 3123, 3881, 4753, 5747, 6871, 8133, 9541, 11103, 12827, 14721, 16793, 19051, 21503, 24157, 27021, 30103, 33411, 36953, 40737, 44771, 49063, 53621, 58453, 63567, 68971, 74673
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
{a(k): 0 <= k < 4} = divisors of 21:
|
|
LINKS
|
|
|
FORMULA
|
a(n) = C(n,0) + 2*C(n,1) + 2*C(n,2) + 8*C(n,3).
E.g.f.: (1/3)*(4*x^3 + 3*x^2 + 6*x + 3)*exp(x). - G. C. Greubel, Jul 16 2017
|
|
EXAMPLE
|
Differences of divisors of 21 to compute the coefficients of their interpolating polynomial, see formula:
1 3 7 21
2 4 14
2 10
8
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(4n^3-9n^2+11n+3)/3, {n, 0, 40}] (* or *)
CoefficientList[Series[(7x^3+x^2-x+1)/(x-1)^4, {x, 0, 60}], x] (* Harvey P. Dale, Mar 28 2011 *)
|
|
PROG
|
(Magma) [(4*n^3 - 9*n^2 + 11*n + 3)/3: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|