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

%I #15 Sep 08 2022 08:45:49

%S 1,1,9,81,6561,531441,387420489,282429536481,1853020188851841,

%T 12157665459056928801,717897987691852588770249,

%U 42391158275216203514294433201,22528399544939174411840147874772641,11972515182562019788602740026717047105681

%N a(n) = 3^floor(n^2/2).

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

%H G. C. Greubel, <a href="/A168493/b168493.txt">Table of n, a(n) for n = 0..50</a>

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

%t Table[3^Floor[n^2/2],{n,0,20}] (* _Harvey P. Dale_, Mar 06 2011 *)

%o (Magma) [3^Floor(n^2/2): n in [0..15]]; // _Vincenzo Librandi_, Jul 24 2016

%K easy,nonn

%O 0,3

%A _Paul Barry_, Nov 27 2009