A099202 - OEIS

%I #17 Jan 18 2023 14:24:43

%S 1,1,4,16,256,4096,262144,16777216,4294967296,1099511627776,

%T 1125899906842624,1152921504606846976,4722366482869645213696,

%U 19342813113834066795298816,316912650057057350374175801344

%N a(n) = 2^floor(n^2/2).

%C Hankel transform of A168490. Linked to elliptic curve y^2=1-12x+44x^2-48x^3 through g.f. of A168490.- _Paul Barry_, Nov 27 2009

%H Vincenzo Librandi, <a href="/A099202/b099202.txt">Table of n, a(n) for n = 0..80</a>

%F a(n) = A016116(n) * A006125(n)

%F a(n) = 16a(n-2)^2 / a(n-4). - _Michael Somos_, Sep 16 2005

%F a(n) = 4^floor(n^2/4) = 4^A002620(n). - _Paul Barry_, Nov 27 2009

%o (PARI) a(n)=2^(n^2\2)

%o (Magma) [2^Floor(n^2/2): n in [0..20]]; // _Vincenzo Librandi_, Aug 16 2011

%o (Python)

%o def A099202(n): return 1<<(n**2>>1) # _Chai Wah Wu_, Jan 18 2023

%Y Cf. A002620, A006125, A016116, A168490.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 04 2004