A168490 -id:A168490 - cp's OEIS frontend

A168511 Triangle T(n,k), read by rows, given by [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,...] DELTA [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 0, 2, 0, 0, 1, 4, 0, 0, 2, 4, 8, 0, 0, 4, 10, 12, 16, 0, 0, 8, 24, 36, 32, 32, 0, 0, 16, 56, 101, 112, 80, 64, 0, 0, 32, 128, 270, 360, 320, 192, 128, 0, 0, 64, 288, 696, 1086, 1160, 864, 448, 256, 0, 0, 128, 640, 1744, 3120, 3900, 3488, 2240, 1024, 512

Offset: 0

Philippe Deléham, Nov 28 2009

			Triangle begins:
  1;
  0, 1;
  0, 0,  2;
  0, 0,  1,  4;
  0, 0,  2,  4,   8;
  0, 0,  4, 10,  12,  16;
  0, 0,  8, 24,  36,  32, 32;
  0, 0, 16, 56, 101, 112, 80, 64;
  ...

Alois P. Heinz, Rows n = 0..140, flattened

Cf. A021913, A133872.

Sum_{k=0..n} T(n,k)*x^(n-k) = A001405(n), A011782(n), A000108(n), A168490(n), A168492(n) for x = -1,0,1,2,3 respectively.

Corrected and extended by Philippe Deléham, Mar 20 2013

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

Original entry on oeis.org

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

Offset: 0

Paul Barry, Oct 04 2004

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

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

Cf. A002620, A006125, A016116, A168490.

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

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

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

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

cp's OEIS Frontend

A168511 Triangle T(n,k), read by rows, given by [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,...] DELTA [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,...] where DELTA is the operator defined in A084938.

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

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