A161710 a(n) = (-6*n^7 + 154*n^6 - 1533*n^5 + 7525*n^4 - 18879*n^3 + 22561*n^2 - 7302*n + 2520)/2520.

1, 2, 3, 4, 6, 8, 12, 24, 39, -2, -295, -1308, -3980, -9996, -22150, -44808, -84483, -150534, -256001, -418588, -661806, -1016288, -1521288, -2226376, -3193341, -4498314, -6234123, -8512892, -11468896, -15261684, -20079482, -26142888

Offset

0,2

Comments

{a(k): 0 <= k < 8} = divisors of 24:

a(n) = A027750(A006218(23) + k + 1), 0 <= k < A000005(24).

Links

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

Reinhard 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,4) - 3*C(n,5) + 8*C(n,6) - 12*C(n,7).

G.f.: (1-6*x+15*x^2-20*x^3+16*x^4-12*x^5+18*x^6-24*x^7)/(1-x)^8. - Bruno Berselli, Jul 17 2011

a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=6, a(5)=8, a(6)=12, a(7)=24, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+ 8*a(n-7)- a(n-8). - Harvey P. Dale, Jul 15 2012

Example

Differences of divisors of 24 to compute the coefficients of their interpolating polynomial, see formula:
1 ... 2 ... 3 ... 4 ... 6 ... 8 .. 12 .. 24
.. 1 ... 1 ... 1 ... 2 ... 2 ... 4 .. 12
..... 0 ... 0 ... 1 ... 0 ... 2 ... 8
........ 0 ... 1 .. -1 ... 2 ... 6
........... 1 .. -2 ... 3 ... 4
............. -3 ... 5 ... 1
................. 8 .. -4
.................. -12.

Mathematica

Table[(-6n^7+154n^6-1533n^5+7525n^4-18879n^3+22561n^2-7302n+2520)/2520, {n, 0, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 3, 4, 6, 8, 12, 24}, 40] (* Harvey P. Dale, Jul 15 2012 *)

Prog

(Magma) [(-6*n^7 + 154*n^6 - 1533*n^5 + 7525*n^4 - 18879*n^ 3 + 22561*n^2 - 7302*n + 2520)/2520: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
(Python)
A161710_list, m = [1], [-12, 80, -223, 333, -281, 127, -23, 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) a(n)=(-6*n^7+154*n^6-1533*n^5+7525*n^4-18879*n^3+22561*n^2-7302*n+2520)/2520 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A080856, A161711, A161712, A161713, A161715, A006261, A018253, A161700, A161856.

Sequence in context: A018597 A018623 A018703 * A018758 A068597 A294342

Adjacent sequences: A161707 A161708 A161709 * A161711 A161712 A161713

Keyword

sign,easy

Author

Reinhard Zumkeller, Jun 17 2009

Status

approved