login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122574 a(1) = a(2) = 1, a(n) = -11a(n-1) + a(n-2). 2

%I

%S 1,1,-10,111,-1231,13652,-151403,1679085,-18621338,206513803,

%T -2290273171,25399518684,-281684978695,3123934284329,-34644962106314,

%U 384218517453783,-4261048654097927,47255753712530980,-524074339491938707,5812073488123856757,-64456882708854363034

%N a(1) = a(2) = 1, a(n) = -11a(n-1) + a(n-2).

%C Characteristic polynomial x^10+11*x^5-1 from the dodecahedral elliptic invariant j(x)=(x^20-228*x^15+494*x^10+228*x^5+1)^3/(-1728*x^5*(x^10+11*x^5-1)^5).

%D Harry Hochstadt, The Functions of Mathematical Physics, Wiley, New York (1971), p. 170; also Dover, New York (1986),129-130

%H Indranil Ghosh, <a href="/A122574/b122574.txt">Table of n, a(n) for n = 1..958</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-11,1).

%F |a(n)| = A049666(n-1)-A049666(n-2), n>1. [_R. J. Mathar_, Nov 02 2008]

%F G.f.: (x+12*x^2)/(1+11*x-x^2). [_Philippe Deléham_, Nov 20 2008]

%F a(n) = (13/50)*sqrt(5)*{[ -(11/2)+(5/2)*sqrt(5)]^(n-1)-[ -(11/2)-(5/2)*sqrt(5)]^(n-1)} +(1/2)*{[ -(11/2)+(5/2)*sqrt(5)]^(n-1)+[ -(11/2)-(5/2)*sqrt(5))^(n-1)}, with n>=1 [_Paolo P. Lava_, Feb 11 2009]

%t a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[6] = 1; a[7] = 1; a[8] = 1; a[9] = 1; a[n_] := a[n] = -11*a[n - 5] + a[n - 10] Table[a[5*n], {n, 0, 50}]

%t LinearRecurrence[{-11,1},{1,1},30] (* _Harvey P. Dale_, Aug 11 2017 *)

%K sign,easy

%O 1,3

%A _Roger L. Bagula_, Sep 17 2006

%E Edited by _N. J. A. Sloane_, Dec 04 2006

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)