login
A185018
Inverse to sequence matrix for natural numbers.
9
1, -2, 1, 1, -2, 1, 0, 1, -2, 1, 0, 0, 1, -2, 1, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1
OFFSET
0,2
COMMENTS
Riordan array ((1-x)^2,x). Inverse matrix is Riordan array (1/(1-x)^2,x), A004736. Row sums are (1,-1,0,0,0,0,0,0,0,0,0,...). Diagonal sums are (1,-2,2,-2,2,-2,2,-2,2,-2,2,...).
FORMULA
T(n,n)=1, T(n,n-1)=-2, T(n,n-2)=1, T(n,k)=0 where k<n-2.
EXAMPLE
Triangle begins :
1 ;
-2, 1 ;
1, -2, 1 ;
0, 1, -2, 1 ;
0, 0, 1, -2, 1 ;
0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 0, 0, 1, -2, 1 ;
MATHEMATICA
Array[PadLeft[{1, -2, 1}, #] &, 15] (* Paolo Xausa, Jun 27 2024 *)
CROSSREFS
Cf. A004736, A167194 (unsigned version).
Sequence in context: A015131 A282716 A167194 * A333289 A099075 A366835
KEYWORD
easy,sign,tabl
AUTHOR
Philippe Deléham, Oct 12 2011
STATUS
approved