%I #16 Jun 28 2024 04:22:31

%S 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,

%T 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,

%U -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

%N Inverse to sequence matrix for natural numbers.

%C 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,...).

%F T(n,n)=1, T(n,n-1)=-2, T(n,n-2)=1, T(n,k)=0 where k<n-2.

%e Triangle begins :

%e 1 ;

%e -2, 1 ;

%e 1, -2, 1 ;

%e 0, 1, -2, 1 ;

%e 0, 0, 1, -2, 1 ;

%e 0, 0, 0, 1, -2, 1 ;

%e 0, 0, 0, 0, 1, -2, 1 ;

%e 0, 0, 0, 0, 0, 1, -2, 1 ;

%e 0, 0, 0, 0, 0, 0, 1, -2, 1 ;

%t Array[PadLeft[{1, -2, 1}, #] &, 15] (* _Paolo Xausa_, Jun 27 2024 *)

%Y Cf. A004736, A167194 (unsigned version).

%K easy,sign,tabl

%O 0,2

%A _Philippe Deléham_, Oct 12 2011