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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 4} = divisors of 21:

a(n) = A027750(A006218(20) + k + 1), 0 <= k < A000005(21).

LINKS

Table of n, a(n) for n=0..39.

R. 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) + 2*C(n,2) + 8*C(n,3).

G.f.: (7x^3+x^2-x+1)/(x-1)^4. - Harvey P. Dale, Mar 28 2011

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

Cf. A000005, A006218, A027750.

Sequence in context: A036569 A018303 A098545 * A192068 A151267 A262184

Adjacent sequences:  A161704 A161705 A161706 * A161708 A161709 A161710

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified May 23 06:21 EDT 2017. Contains 286909 sequences.