|
| |
|
|
A132772
|
|
a(n) = n*(n + 30).
|
|
2
|
|
|
|
0, 31, 64, 99, 136, 175, 216, 259, 304, 351, 400, 451, 504, 559, 616, 675, 736, 799, 864, 931, 1000, 1071, 1144, 1219, 1296, 1375, 1456, 1539, 1624, 1711, 1800, 1891, 1984, 2079, 2176, 2275, 2376, 2479, 2584, 2691, 2800, 2911, 3024, 3139, 3256, 3375, 3496, 3619
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
G.f.: x*(-31+29*x)/(-1+x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=31, a(2)=64, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 06 2015
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)
|
|
|
MATHEMATICA
|
Table[n(n+30), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 31, 64}, 50] (* Harvey P. Dale, Mar 06 2015 *)
|
|
|
PROG
|
(PARI) a(n)=n*(n+30) \\ Charles R Greathouse IV, Jun 17 2017
|
|
|
CROSSREFS
|
Cf. A001008, A002378, A102928, A120071, A067079, A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770, A132771, A098849, A098850, A005563, A028552, A028347, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A132759, A098848.
Sequence in context: A042918 A042920 A247438 * A116324 A179571 A044133
Adjacent sequences: A132769 A132770 A132771 * A132773 A132774 A132775
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Omar E. Pol, Aug 28 2007
|
|
|
STATUS
|
approved
|
| |
|
|
