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A161715 a(n) = (50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040. 21
1, 2, 3, 5, 6, 10, 15, 30, 171, 886, 3359, 10143, 26072, 59502, 123931, 240048, 438261, 761754, 1270123, 2043641, 3188202, 4840994, 7176951, 10416034, 14831391, 20758446, 28604967, 38862163, 52116860, 69064806, 90525155, 117456180 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{a(k): 0 <= k < 8} = divisors of 30:

a(n) = A027750(A006218(29) + k + 1), 0 <= k < A000005(30).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

R. Zumkeller, Enumerations of Divisors

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n) = C(n,0) + C(n,1) + C(n,3) - 3*C(n,4) + 9*C(n,5) - 21*C(n,6) + 50*C(n,7).

G.f.: (1-6*x+15*x^2-19*x^3+8*x^4+18*x^5-51*x^6+84*x^7)/(-1+x)^8. - R. J. Mathar, Jun 18 2009

EXAMPLE

Differences of divisors of 30 to compute the coefficients of their interpolating polynomial, see formula:

  1     2     3     5     6    10    15    30

     1     1     2     1     4     5    15

        0     1    -1     3     1    10

           1    -2     4    -2     9

             -3     6    -6    11

                 9   -12    17

                  -21    29

                      50

MATHEMATICA

CoefficientList[Series[(1-6*x+15*x^2-19*x^3+8*x^4+18*x^5-51*x^6+84*x^7)/(-1+x)^8, {x, 0, 50}], x] (* G. C. Greubel, Jul 16 2017 *)

PROG

(MAGMA) [(50*n^7 - 1197*n^6 + 11333*n^5 - 53655*n^4 + 132125*n^3 - 156828*n^2 + 73212*n + 5040)/5040: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011

(Python)

A161710_list, m = [1], [50, -321, 864, -1249, 1024, -452, 85, 1]

for _ in range(1, 10**2):

....for i in range(7):

........m[i+1]+= m[i]

....A161710_list.append(m[-1]) # Chai Wah Wu, Nov 09 2014

(PARI) x='x+O('x^50); Vec((1 -6*x +15*x^2 -19*x^3 +8*x^4 +18*x^5 -51*x^6 +84*x^7) /(-1+x)^8) \\ G. C. Greubel, Jul 16 2017

CROSSREFS

Cf. A000124, A000125, A000127, A002522, A005408, A006261, A016813, A058331, A080856, A086514, A161701, A161702, A161703, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713.

Cf. A018255, A161700, A161856. - Reinhard Zumkeller, Jun 21 2009

Sequence in context: A018255 A194358 A018727 * A164523 A227305 A240949

Adjacent sequences:  A161712 A161713 A161714 * A161716 A161717 A161718

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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Last modified July 21 03:02 EDT 2017. Contains 289629 sequences.