|
| |
|
|
A161712
|
|
(4*n^3 - 6*n^2 + 8*n + 3)/3.
|
|
19
| |
|
|
1, 3, 9, 27, 65, 131, 233, 379, 577, 835, 1161, 1563, 2049, 2627, 3305, 4091, 4993, 6019, 7177, 8475, 9921, 11523, 13289, 15227, 17345, 19651, 22153, 24859, 27777, 30915, 34281, 37883, 41729, 45827, 50185, 54811, 59713, 64899, 70377, 76155
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| {a(k): 0 <= k < 4} = divisors of 27:
a(n) = A027750(A006218(26) + k + 1), 0 <= k < A000005(27).
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
R. Zumkeller, Enumerations of Divisors
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
|
|
|
FORMULA
| a(n) = C(n,0) + 2*C(n,1) + 4*C(n,2) + 8*C(n,3).
G.f.: ((x+1)(1+x(5x-2)))/(x-1)^4 [From Harvey P. Dale, Apr 13 2011]
|
|
|
EXAMPLE
| Differences of divisors of 27 to compute the coefficients of their interpolating polynomial, see formula:
1 ... 3 ... 9 ... 27
.. 2 ... 6 .. 18
..... 4 .. 12
........ 8.
|
|
|
MATHEMATICA
| Table[(4n^3-6n^2+8n+3)/3, {n, 0, 80}] (* From Harvey P. Dale, Apr 13 2011 *)
|
|
|
PROG
| (PARI) a(n)=(4*n^3-6*n^2+8*n)/3+1 \\ Charles R Greathouse IV, Jul 16, 2011
(MAGMA) [(4*n^3 - 6*n^2 + 8*n + 3)/3: n in [0..40]]; // Vincenzo Librandi, Jul 17 2011
|
|
|
CROSSREFS
| Sequence in context: A015955 A097803 A201202 * A137368 A191007 A036215
Adjacent sequences: A161709 A161710 A161711 * A161713 A161714 A161715
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009
|
| |
|
|
