A121814 A 3 X 3 determinant based recursion.

0, 1, 1, -2, 0, 7, -335, 37595032, -53136308105121335327856, 150028625138472351236334849506272469590820016866180023237071134409583

Offset

1,4

Comments

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

[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)]. - Robert Israel, Nov 13 2017

Links

Robert Israel, Table of n, a(n) for n = 1..12

Formula

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.

Maple

A[1]:= 0: A[2]:= 1: A[3]:= 1:
for n from 4 to 12 do
  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]>>)
od:
seq(A[i], i=1..12); # Robert Israel, Nov 13 2017

Mathematica

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}]

Crossrefs

Sequence in context: A016631 A164269 A293265 * A195298 A010581 A356920

Adjacent sequences: A121811 A121812 A121813 * A121815 A121816 A121817

Keyword

sign

Author

Roger L. Bagula, Aug 30 2006

Extensions

Edited by Robert Israel, Nov 13 2017

Status

approved