A099202 a(n) = 2^floor(n^2/2).

1, 1, 4, 16, 256, 4096, 262144, 16777216, 4294967296, 1099511627776, 1125899906842624, 1152921504606846976, 4722366482869645213696, 19342813113834066795298816, 316912650057057350374175801344, 5192296858534827628530496329220096, 340282366920938463463374607431768211456

Offset: 0

Author

Paul Barry, Oct 04 2004

Keywords

• easy
• nonn

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A002620, A006125, A016116, A168490.

Programs

Magma

[2^Floor(n^2/2): n in [0..20]]; // Vincenzo Librandi, Aug 16 2011

PARI

a(n)=2^(n^2\2)

Python

def A099202(n): return 1<<(n**2>>1) # Chai Wah Wu, Jan 18 2023

Formula

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

a(n) = 16*a(n-2)^2 / a(n-4). - Michael Somos, Sep 16 2005

a(n) = 4^floor(n^2/4) = 4^A002620(n). - Paul Barry, Nov 27 2009