|
| |
| |
|
|
|
0, 5, 12, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320, 357, 396, 437, 480, 525, 572, 621, 672, 725, 780, 837, 896, 957, 1020, 1085, 1152, 1221, 1292, 1365, 1440, 1517, 1596, 1677, 1760, 1845, 1932, 2021, 2112, 2205, 2300, 2397, 2496, 2597
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,2
|
|
|
COMMENTS
|
Sequence allows us to find X values of the equation: X^3 + 4*X^2 = Y^2. To find Y values: b(n)=n*(n^2 - 4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
Discriminants of binary forms x^2 + n*x*y + y^2 (for n>1) - Artur Jasinski, Apr 28 2008
Number of units of a(n) belongs to a periodic sequence: 0, 5, 2, 1, 2, 5, 0, 7, 6, 7. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 04 2009]
a(n)*a(n-1)+4 = (a(n)-n)^2. This is the case d=4 in the general (n^2-d)*((n-1)^2-d)+d = (n^2-n-d)^2. - Bruno Berselli, Dec 07 2011
|
|
|
REFERENCES
|
A. Connes, Noncommutative Geometry, Academic Press, 1994, p. 35.
|
|
|
LINKS
|
Table of n, a(n) for n=2..51.
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013
Eric Weisstein's World of Mathematics, Near-Square Prime
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
Except for initial term, denominators of energies of hydrogen lines.
a(n+2) = n(n+4). G.f. x^3*(5-3*x)/(1-x)^3. - Barry E. Williams, Jun 16 2000, R. J. Mathar, Aug 06 2009
a(n) = 2*n+a(n-1)-1. - Vincenzo Librandi, Aug 02 2010
sum_{n>=3} 1/a(n) = 25/48 = 0.52083333.. = 100*A021196. - R. J. Mathar, Mar 22 2011
a(n) = x, the solution of k=(sqrt(x)+n)/2 and k+(1/k)=n (also valid for a(0)=-4 and a(1)=-3). - Charles L. Hohn, Apr 16 2011
|
|
|
MATHEMATICA
|
Table[n^2-4, {n, 2, 100}] (* Vladimir Joseph Stephan Orlovsky, Nov 06 2008 *)
|
|
|
CROSSREFS
|
a(n), n>=3, second column (used for the Balmer series of the hydrogen atom) of triangle A120070.
Cf. A005563, A046092, A001082, A002378, A036666, A062717.
Sequence in context: A063559 A121291 A097984 * A038794 A225284 A217649
Adjacent sequences: A028344 A028345 A028346 * A028348 A028349 A028350
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
