0,3

Used when showing that the regular simplex is not "scisssors-dissectable" to a cube, thus answering Hilbert's third problem.

J. L. Dupont, Scissors Congruences, Group Homology and Characteristic Classes, World Scientific, 2001. See p. 4.

a(0) = 1, a(1) = 1; for n >= 2, a(n) = 2*a(n-1) - 9*a(n-2). - Warut Roonguthai (warut822(AT)yahoo.com), Oct 11 2005

a(n) = (1/2)*(1-2*i*2^(1/2))^(n+1)+(1/2)*(1+2*i*2^(1/2))^(n+1), where i=sqrt(-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2003

a(n) is the permanent of the matrix M^n, where M = [i, 2; 1, i]. - Simone Severini (simoseve(AT)gmail.com), Apr 27 2007

f:=proc(n) option remember; if n <= 1 then RETURN(1); fi; 2*f(n-1)-9*f(n-2); end;

Table[ n/2 3^n GegenbauerC[ n, 1/3 ], {n, 24} ]

(PARI) {a(n)= if(n<0, 0, 3^(n-1)* subst(3* poltchebi(abs(n)), x, 1/3))} /* Michael Somos Mar 14 2007 */

Sequence in context: A070411 A167224 A121815 this_sequence A115023 A009228 A031450

Adjacent sequences: A025169 A025170 A025171 this_sequence A025173 A025174 A025175

sign

Wouter Meeussen (wouter.meeussen(AT)pandora.be)

Better description from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2003

Edited by N. J. A. Sloane (njas(AT)research.att.com), Feb 22 2007. Among other things, I changed the offset and the beginning of the sequence, so some of the formulae may need to be adjusted slightly.