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A161704 (3n^5 - 35n^4 + 145n^3 - 235n^2 + 152n + 30)/30. 19
1, 2, 3, 6, 9, 18, 59, 190, 513, 1186, 2435, 4566, 7977, 13170, 20763, 31502, 46273, 66114, 92227, 125990, 168969, 222930, 289851, 371934, 471617, 591586, 734787, 904438, 1104041, 1337394, 1608603, 1922094, 2282625, 2695298, 3165571, 3699270 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 6} = divisors of 18:

a(n) = A027750(A006218(17) + k + 1), 0 <= k < A000005(18).

LINKS

Table of n, a(n) for n=0..35.

R. Zumkeller, Enumerations of Divisors

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = C(n,0) + C(n,1) + 2*C(n,3) - 4*C(n,4) + 12*C(n,5).

G.f.: ( 1-4*x+6*x^2-2*x^3-7*x^4+18*x^5 ) / (x-1)^6 . - R. J. Mathar, Jul 12 2016

EXAMPLE

Differences of divisors of 18 to compute the coefficients of their interpolating polynomial, see formula:

1 ... 2 ... 3 ... 6 ... 9 ... 18

.. 1 ... 1 ... 3 ... 3 ... 9

..... 0 ... 2 ... 0 ... 6

........ 2 .. -2 ... 6

.......... -4 ... 8

............. 12.

PROG

(MAGMA)[(3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30: n in [0..50]]; [From Vincenzo Librandi, Dec 27 2010]

(PARI) a(n)=n*(3*n^4-35*n^3+145*n^2-235*n+152)/30+1

CROSSREFS

Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161706, A161707, A161708, A161710, A080856, A161711, A161712, A161713, A161715, A006261, A018251, A161856.

Sequence in context: A032251 A018679 A018741 * A011962 A060172 A193196

Adjacent sequences:  A161701 A161702 A161703 * A161705 A161706 A161707

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.