|
| |
|
|
A106328
|
|
Numbers j such that 8*(j^2) + 9 = k^2 for some positive number k.
|
|
3
| |
|
|
0, 3, 18, 105, 612, 3567, 20790, 121173, 706248, 4116315, 23991642, 139833537, 815009580, 4750223943, 27686334078, 161367780525, 940520349072, 5481754313907, 31950005534370, 186218278892313, 1085359667819508, 6325939728024735
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The ratio k(n) /(2*j(n)) tends to sqrt(2) as n increases.
The squares of the numbers in this sequence are one less than a triangular number: a(n)^2 = A164080(n). For example, 18^2 is 324, and 325 is a triangular number. a(n)^2 + 1 = A164055(n). a(n)^2 = A072221(n)(A072221(n)+1)/2 - 1. [From Tanya Khovanova & Alexey Radul (tanyakh(AT)yahoo.com), Aug 09 2009]
|
|
|
LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (6,-1).
Tanya Khovanova, Recursive Sequences
|
|
|
FORMULA
| a(1)=0, a(2)=3 then a(n) = 6*a(n-1) - a(n-2).
a(n) = ((3+2*sqrt(2))^(n-1) - (3-2*sqrt(2))^(n-1))*3/4/sqrt(2). - Max Alekseyev (maxale(AT)gmail.com), Jan 11 2007
a(n) = 3*A001109(n) [M. Hasler, R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
a(n) = (3/4)*A005319(n-1).
G.f.: 3x^2/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
|
|
|
MATHEMATICA
| s=0; lst={}; Do[s+=n; If[Sqrt[s-1]==Floor[Sqrt[s-1]], AppendTo[lst, Sqrt[s-1]]], {n, 8!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 02 2009]
|
|
|
PROG
| (Haskell)
a106328 n = a106328_list !! (n-1)
a106328_list = 0 : 3 : zipWith (-) (map (* 6) (tail a106328_list)) a106328_list
-- Reinhard Zumkeller, 10 Jan 2012
|
|
|
CROSSREFS
| Cf. A103328, A164080, A164055, A072221. [From Tanya Khovanova & Alexey Radul (tanyakh(AT)yahoo.com), Aug 09 2009]
Sequence in context: A009021 A124408 A136779 * A007277 A025595 A151331
Adjacent sequences: A106325 A106326 A106327 * A106329 A106330 A106331
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Pierre CAMI (pierre-cami(AT)bbox.fr), Apr 29 2005
|
|
|
EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Jan 11 2007
|
| |
|
|
