Search: id:A122574
Results 1-1 of 1 results found.

%I A122574
%S A122574 1,1,10,111,1231,13652,151403,1679085,18621338,206513803,2290273171,25399518684,
%T A122574 281684978695,3123934284329,34644962106314,384218517453783,4261048654097927,
%U A122574 47255753712530980,524074339491938707,5812073488123856757,64456882708854363034
%V A122574 1,1,-10,111,-1231,13652,-151403,1679085,-18621338,206513803,-2290273171,
               25399518684,
%W A122574 -281684978695,3123934284329,-34644962106314,384218517453783,-4261048654097927,
%X A122574 47255753712530980,-524074339491938707,5812073488123856757,-64456882708854363034
%N A122574 a(1)=a(2)=1, a(n)=-11a(n-1)+a(n-2)
%C A122574 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 A122574 Harry Hochstadt, The Functions of Mathematical Physics, Wiley, New York 
               (1971), p. 170; also Dover, New York (1986),129-130
%H A122574 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A122574 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A122574 |a(n)| = A049666(n-1)-A049666(n-2), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 02 2008]
%F A122574 G.f.: (x+12*x^2)/(1+11*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 20 2008]
%F A122574 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 [From Paolo P. Lava (ppl(AT)spl.at), Feb 11 2009]
%t A122574 M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, 
               {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 
               0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 
               0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 
               0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, -11, 0, 0, 0, 0}} v[1] = Table[1, 
               {n, 0, 9}] v[n_] := v[n] = M.v[n - 1] a1 = Table[Floor[v[5*n][[1]]], 
               {n, 1, 25}] (* alternative*) 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}]
%Y A122574 Sequence in context: A078252 A014993 A015592 this_sequence A084031 A066275 
               A046164
%Y A122574 Adjacent sequences: A122571 A122572 A122573 this_sequence A122575 A122576 
               A122577
%K A122574 sign
%O A122574 1,3
%A A122574 Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006
%E A122574 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006

Search completed in 0.001 seconds