|
| |
|
|
A028884
|
|
a(n) = (n + 3)^2 - 8.
|
|
15
|
|
|
|
1, 8, 17, 28, 41, 56, 73, 92, 113, 136, 161, 188, 217, 248, 281, 316, 353, 392, 433, 476, 521, 568, 617, 668, 721, 776, 833, 892, 953, 1016, 1081, 1148, 1217, 1288, 1361, 1436, 1513, 1592, 1673, 1756, 1841, 1928, 2017, 2108, 2201, 2296, 2393
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Altug Alkan, Table of n, a(n) for n = 0..10000
Patrick De Geest, Palindromic Quasipronics of the form n(n+x)
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
a(n) = a(n-1) + 2*n + 5 (with a(0) = 1). - Vincenzo Librandi, Aug 05 2010
a(n) = A028560(n) + 1; A014616(n) = floor(a(n+1)/4). - Reinhard Zumkeller, Apr 07 2013
G.f.: ( -1 - 5*x + 4*x^2 ) / (x-1)^3. - R. J. Mathar, Mar 24 2013
Sum_{n >= 0} 1/a(n) = 51/112 - Pi*cot(2*Pi*sqrt(2))/(4*sqrt(2)) = 1.3839174974448... . - Vaclav Kotesovec, Apr 10 2016
E.g.f.: (1 + 7*x + x^2)*exp(x). - G. C. Greubel, Aug 19 2017
Sum_{n >= 0} (-1)^n/a(n) = (-19 + 14*sqrt(2)*Pi*cosec(2*sqrt(2)*Pi)/112. - Amiram Eldar, Nov 04 2020
|
|
|
MATHEMATICA
|
Range[3, 50]^2 - 8 (* Alonso del Arte, Aug 15 2016 *)
|
|
|
PROG
|
(Haskell)
a014616 n = (n * (n + 6) + 1) `div` 4 -- Reinhard Zumkeller, Apr 07 2013
(PARI) a(n)=(n+3)^2-8 \\ Charles R Greathouse IV, Oct 07 2015
(Scala) (3 to 49).map(n => n * n - 8) // Alonso del Arte, May 07 2020
|
|
|
CROSSREFS
|
Cf. A005563.
Sequence in context: A190749 A056121 A264355 * A322473 A247117 A099358
Adjacent sequences: A028881 A028882 A028883 * A028885 A028886 A028887
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Patrick De Geest
|
|
|
EXTENSIONS
|
Definition corrected by Omar E. Pol, Jul 27 2009
|
|
|
STATUS
|
approved
|
| |
|
|
