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A121814 A 3 X 3 determinant based recursion. 1

%I #9 Nov 13 2017 21:56:52

%S 0,1,1,-2,0,7,-335,37595032,-53136308105121335327856,

%T 150028625138472351236334849506272469590820016866180023237071134409583

%N A 3 X 3 determinant based recursion.

%C For n >= 3, a(n) is the determinant of the matrix

%C [a(n-3),a(n-1),a(n-2)]

%C [a(n-1),a(n-2),a(n-3)]

%C [a(n-2),a(n-3),a(n-1)]. - _Robert Israel_, Nov 13 2017

%H Robert Israel, <a href="/A121814/b121814.txt">Table of n, a(n) for n = 1..12</a>

%F a(n) = 3*a(n-1)*a(n-2)*a(n-3)-a(n-1)^3-a(n-2)^3-a(n-3)^3 for n >= 4.

%p A[1]:= 0: A[2]:= 1: A[3]:= 1:

%p for n from 4 to 12 do

%p A[n]:= LinearAlgebra:-Determinant(<<A[n-3],A[n-1],A[n-2]>|<A[n-1],A[n-2],A[n-3]>|<A[n-2],A[n-3],A[n-1]>>)

%p od:

%p seq(A[i],i=1..12); # _Robert Israel_, Nov 13 2017

%t M = {{a[n - 3], a[n - 1], a[n - 2]}, {a[n - 1], a[n - 2], a[n - 3]}, {a[n - 2], a[n - 3], a[n - 1]}}; a[0] = 0; a[1] = 1; a[2] = 1; a[n_] := a[n] = Det[M] b = Table[a[n], {n, 0, 10}]

%K sign

%O 1,4

%A _Roger L. Bagula_, Aug 30 2006

%E Edited by _Robert Israel_, Nov 13 2017

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Last modified April 21 07:13 EDT 2024. Contains 371850 sequences. (Running on oeis4.)