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A161715 (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.

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

CROSSREFS

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

Cf. A018255, A161700, A161856. [From 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

AUTHOR

Reinhard Zumkeller, Jun 17 2009

STATUS

approved

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