A114284 Riordan array ((1-3*x)/(1-x), x).

1, -2, 1, -2, -2, 1, -2, -2, -2, 1, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1

Offset

0,2

Comments

Inverse of A114283. Row sums are 1-2n. Diagonal sums are A114285. Sequence array of 3*0^n-2.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

Formula

T(n, k) = if(k<=n, 3*0^(n-k)-2, 0).

a(n) = -3 floor(1/2 sqrt(8 x+1)-1/2)+3 floor(1/2 sqrt(8 x+9)-1/2)-2 (* Jackson Xier, Oct 07 2011 *)

Example

Triangle begins
1;
-2,1;
-2,-2,1;
-2,-2,-2,1;
-2,-2,-2,-2,1;

Mathematica

Table[-2 - 3 Floor[1/2 (-1 + Sqrt[1 + 8 x])] + 3 Floor[1/2 (-1 + Sqrt[9 + 8 x])], {x, 0, 250}] (* Jackson Xier, Oct 07 2011 *)

Crossrefs

Sequence in context: A265404 A274353 A183028 * A238303 A023575 A215113

Adjacent sequences: A114281 A114282 A114283 * A114285 A114286 A114287

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 20 2005

Status

approved