A185018 Inverse to sequence matrix for natural numbers.

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

Author

Philippe Deléham, Oct 12 2011

Keywords

• easy
• sign
• tabl

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,...).

Examples

			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 ;
		

Crossrefs

Cf. A004736, A167194 (unsigned version).

Programs

Mathematica

Array[PadLeft[{1, -2, 1}, #] &, 15] (* Paolo Xausa, Jun 27 2024 *)

Formula

T(n,n)=1, T(n,n-1)=-2, T(n,n-2)=1, T(n,k)=0 where k

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