1,3

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).

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

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

|a(n)| = A049666(n-1)-A049666(n-2), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2008]

G.f.: (x+12*x^2)/(1+11*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]

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]

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}]

Sequence in context: A078252 A014993 A015592 this_sequence A084031 A066275 A046164

Adjacent sequences: A122571 A122572 A122573 this_sequence A122575 A122576 A122577

sign

Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006

Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006