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Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.
0

%I #6 Feb 24 2019 04:36:03

%S 1,-8,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.

%F a(n) = determinant of n X n matrix of first n^2 nonzero terms of A000217(k) for k>0. a(n) = determinant of n X n matrix of k*(k+1)/2 for k from 1 through n^2.

%e a(3) = -27 =

%e |.1..3..6|

%e |10.15.21|

%e |28.36.45|.

%e a(4) = 0 because of the singular matrix 0 =

%e |.1...3...6..10|

%e |15..21..28..36|

%e |45..55..66..78|

%e |91.105.120.136|.

%t nmax = 100; Table[Det[Table[(k*(i-1) + j)*(k*(i-1) + j + 1)/2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Feb 24 2019 *)

%Y Cf. A000217, A119493.

%K easy,sign

%O 1,2

%A _Jonathan Vos Post_, May 27 2006

%E More terms from _Vaclav Kotesovec_, Feb 24 2019