A168492 -id:A168492 - 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

A168493 a(n) = 3^floor(n^2/2).

Original entry on oeis.org

1, 1, 9, 81, 6561, 531441, 387420489, 282429536481, 1853020188851841, 12157665459056928801, 717897987691852588770249, 42391158275216203514294433201, 22528399544939174411840147874772641, 11972515182562019788602740026717047105681

Offset: 0

Paul Barry, Nov 27 2009

Hankel transform of A168492. A trivial Somos-4 sequence linked to elliptic curve y^2 = 1 - 16x + 76x^2 - 96x^3.

G. C. Greubel, Table of n, a(n) for n = 0..50

[3^Floor(n^2/2): n in [0..15]]; // Vincenzo Librandi, Jul 24 2016

Table[3^Floor[n^2/2],{n,0,20}]  (* Harvey P. Dale, Mar 06 2011 *)

a(n) = 3^floor(n^2/2) = 9^floor(n^2/4) = 9^A002620(n) = 81*a(n-2)^2/a(n-4).

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

Extensions

A168493 a(n) = 3^floor(n^2/2).

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

Formula