Sequence 1, 1, 2, 7, 33, 191, 1304, 10241, ...
- Subject: Sequence 1, 1, 2, 7, 33, 191, 1304, 10241, ...
- From: Aleksas Domarkas
- Date: Thu, 27 Oct 2011 09:43:11 +0300
Sequence 1, 1, 2, 7, 33, 191, 1304, 10241, ...
(%i1) h[i,j]:=if i=j then i
elseif abs(i-j)=1 then 1
else 0;
(%o1) h[i,j]:=if i=j then i elseif abs(i-j)=1 then 1 else 0
(%i2) A(n):=genmatrix(lambda([i,j], h[i,j]), n, n);
(%o2) A(n):=genmatrix(lambda([i,j],h[i,j]),n,n)
(%i3) makelist(A(k),k,1,8)$
(%i4) map(determinant,%);
(%o4) [1,1,2,7,33,191,1304,10241]
****************
(%i5) load(solve_rec);
(%o5)
"C:/PROGRA~2/MAXIMA~1.1/share/maxima/5.25.1/share/contrib/solve_rec/solve_rec.mac"
(%i6) solve_rec(d(n)=n*d(n-1)-d(n-2),d(n),d(1)=1,d(2)=1);
(%o6) false
*****************
(%i7) f(n):= if n=1 or n=2 then 1 else n*f(n-1)-f(n-2);
(%o7) f(n):=if n=1 or n=2 then 1 else n*f(n-1)-f(n-2)
(%i8) makelist(f(k),k,1,8);
(%o8) [1,1,2,7,33,191,1304,10241]
******************
(%i9) a(n):=(bessel_j(n,2)*bessel_y(0,2)-bessel_j(0,2)*bessel_y(n,2))/
(bessel_j(1,2)*bessel_y(0,2)-bessel_j(0,2)*bessel_y(1,2))$
(%i10) makelist(a(k),k,1,8)$ float(%);
(%o11)
[1.0,1.0,1.0,2.0,7.000000000000002,33.00000000000001,191.0000000000001,1304.0]
How solve recurence equation d(n)=n*d(n-1)-d(n-2) ?
How simplify a(n) to integer values ?
References:
http://oeis.org/A058797/b058797.txt
Thank you for discussion
Aleksas D