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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
OFFSET
0,2
COMMENTS
{a(k): 0 <= k < 4} = divisors of 21:
a(n) = A027750(A006218(20) + k + 1), 0 <= k < A000005(21).
FORMULA
a(n) = C(n,0) + 2*C(n,1) + 2*C(n,2) + 8*C(n,3).
G.f.: (7*x^3 + x^2 - x + 1)/(x-1)^4. - Harvey P. Dale, Mar 28 2011
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
A161707:=n->(4*n^3 - 9*n^2 + 11*n + 3)/3: seq(A161707(n), n=0..100); # Wesley Ivan Hurt, Jan 19 2017
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
(PARI) a(n)=(4*n^3-9*n^2+11*n)/3+1 \\ Charles R Greathouse IV, Jul 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jun 17 2009
STATUS
approved