A071999 Determinant of n X n matrix whose element A(i,j) is 1 if i=j, i if n=i+j and 0 otherwise.

1, 1, -1, -2, 15, 28, -495, -924, 29393, 55200, -2755377, -5206760, 374909535, 712318464, -69864169375, -133355433456, 17088978269025, 32747341496320, -5311777786094241, -10212994682100000, 2045230826019387119, 3943711514611814400, -955583772509043759375

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

a(n) ~ -(-1)^(n*(n+1)/2) * ((n-2)! * (1 + (-1)^n) + (n-1)! * (1 - (-1)^n)/2). - Vaclav Kotesovec, Jan 08 2019

Maple

with(LinearAlgebra):
a:= n-> Determinant(Matrix(n, (i, j)->
       `if`(i=j, 1, `if`(n=i+j, i, 0)))):
seq(a(n), n=1..25);  # Alois P. Heinz, Nov 13 2015

Mathematica

Table[ Det[ Table[ If[i == j, 1, If[n == j + i, i, 0]], {i, 1, n}, {j, 1, n}]], {n, 1, 22}]

Prog

(PARI) a(n) = matdet(matrix(n, n, i, j, if(i==j, 1, if(n==i+j, i, 0)))) \\ Colin Barker, Nov 13 2015

Crossrefs

Sequence in context: A212975 A128828 A032002 * A031289 A093917 A076352

Adjacent sequences: A071996 A071997 A071998 * A072000 A072001 A072002

Keyword

sign

Author

Robert G. Wilson v, Jun 19 2002

Status

approved