|
Search: id:A058799
|
|
| |
|
| 1, 3, 11, 52, 301, 2055, 16139, 143196, 1415821, 15430835, 183754199, 2373373752, 33043478329, 493278801183, 7859417340599, 133116815989000, 2388243270461401, 45243505322777619, 902481863185090979
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
Weisstein, Eric W. "Modular Group Gamma." http : // mathworld.wolfram.com/ModularGroupGamma.html [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008]
|
|
FORMULA
|
a(n) =(n+2)*a(n-1)-a(n-2) [with a(0)=1 and a(-1)=0] =A058798(n+1)-A058797(n+2) - Henry Bottomley (se16(AT)btinternet.com), Feb 28 2001
A signed version with a slightly different start may be obtained from the modular group Gamma: Let S = {{0, -1}, {1, 0}}; T = {{1, 1}, {0, 1}}; m(n)=T^n.S.m(m-1); v(0)={1,0}; v(n)=m(n).v(0); a(n)=v(n)[[1]]. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008]
|
|
MATHEMATICA
|
Clear[S, T, M, v, n]; S = {{0, -1}, {1, 0}}; T = {{1, 1}, {0, 1}}; M[0] = T.S; M[n_] := M[n] = (MatrixPower[T, n].S).M[n - 1]; v[0] = {1, 0}; v[n_] := v[n] = M[n].v[0]; a = Table[v[n][[1]], {n, 0, 30}] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008]
|
|
CROSSREFS
|
Sequence in context: A007047 A129097 A014510 this_sequence A054362 A129833 A107958
Adjacent sequences: A058796 A058797 A058798 this_sequence A058800 A058801 A058802
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Christian G. Bower (bowerc(AT)usa.net), Dec 02 2000
|
|
|
Search completed in 0.002 seconds
|
