OFFSET
0,2
COMMENTS
Hankel transform of A157004.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..145
FORMULA
a(n) = (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(0)=1, a(1)=2, a(2)=8, a(3)=24.
a(n) = 2^n*A006720(n+2).
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==2, a[2]==8, a[3]==24, a[n]==(a[n-1] a[n-3]+a[n-2]^2)/a[n-4]}, a, {n, 20}] (* Harvey P. Dale, Apr 30 2011 *)
PROG
(PARI) m=20; v=concat([1, 2, 8, 24], vector(m-4)); for(n=5, m, v[n] = (v[n-1]*v[n-3] +v[n-2]^2)/v[n-4]); v \\ G. C. Greubel, Feb 23 2019
(Magma) I:=[1, 2, 8, 24]; [n le 4 select I[n] else (Self(n-1)*Self(n-3) + Self(n-2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Feb 23 2019
(Sage)
def a(n):
if (n==0): return 1
elif (n==1): return 2
elif (n==2): return 8
elif (n==3): return 24
else: return (a(n-1)*a(n-3) + a(n-2)^2)/a(n-4)
[a(n) for n in (0..20)] # G. C. Greubel, Feb 23 2019
(GAP) a:=[1, 2, 8, 24];; for n in [5..20] do a[n]:=(a[n-1]*a[n-3] + a[n-2]^2)/a[n-4]; od; a; # G. C. Greubel, Feb 23 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 20 2009
STATUS
approved