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A144966
Square array T(n,k) read by antidiagonals up. A055615 interleaved with k-1 zeros in each column. Redheffer type matrix.
0
1, -2, 1, -3, 1, 1, 0, 0, 0, 1, -5, -2, 1, 0, 1, 6, 0, 0, 0, 0, 1, -7, -3, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 1, -11, -5, -3, -2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -13, 6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 14, 0, 0, 0, -2, 0
OFFSET
1,2
COMMENTS
Determinant of this array appears to be the triangular numbers. The number of permutations that contribute to the result of the zero corner determinant that give the natural numbers, appears to be given by A002033.
EXAMPLE
Determinant of:
1
is equal to 1.
Determinant of:
1,1
-2,0
is equal to 2.
Determinant of:
1,1,1
-2,1,0
-3,0,0
is equal to 3.
Determinant of:
1,1,1,1
-2,1,0,0
-3,0,1,0
0,-2,0,0
is equal to 4.
Determinant of:
1,1,1,1,1
-2,1,0,0,0
-3,0,1,0,0
0,-2,0,1,0
-5,0,0,0,0
is equal to 5.
Determinant of:
1,1,1,1,1,1
-2,1,0,0,0,0
-3,0,1,0,0,0
0,-2,0,1,0,0
-5,0,0,0,1,0
6,-3,-2,0,0,0
is equal to 6.
PROG
(Excel) =if(mod(row(); column())=0; lookup(row()/column(); A000027; A055615); if(row()=1; 1; 0))
CROSSREFS
Sequence in context: A377038 A376682 A350004 * A320000 A119805 A111957
KEYWORD
sign,tabl
AUTHOR
Mats Granvik, Sep 27 2008
STATUS
approved