login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157623 781250n^2 - 455000n + 66249. 3
392499, 2281249, 5732499, 10746249, 17322499, 25461249, 35162499, 46426249, 59252499, 73641249, 89592499, 107106249, 126182499, 146821249, 169022499, 192786249, 218112499, 245001249, 273452499, 303466249, 335042499, 368181249 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (781250*n^2-455000*n+66249)^2-(625*n^2-364*n+53)*(31250*n-9100)^2=1 can be written as a(n)^2-A157621(n)*A157622(n)^2=1.
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
a(1)=392499, a(2)=2281249, a(3)=5732499, a(n)=3*a(n-1)-3*a(n-2)+ a(n-3) [From Harvey P. Dale, Jul 11 2011]
G.f.: (392499+1103752*x+66249*x^2)/(1-x)^3 [From Harvey P. Dale, Jul 11 2011]
EXAMPLE
For n=1, a(1)=392499; n=2, a(2)=2281249; n=3, a(3)=5732499.
MATHEMATICA
Table[781250n^2-455000n+66249, {n, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {392499, 2281249, 5732499}, 25] (* or *) CoefficientList[Series[ (-392499- 1103752 x-66249 x^2)/(x-1)^3, {x, 0, 25}], x] (* Harvey P. Dale, Jul 11 2011 *)
PROG
(Magma) I:=[392499, 2281249, 5732499]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=781250*n^2-455000*n+66249
CROSSREFS
Sequence in context: A346340 A345638 A346351 * A145228 A204628 A171439
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 03 2009
EXTENSIONS
Minor corrections by M. F. Hasler, Oct 08 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)