A144083 Triangle read by rows: partial sums from the right of an A010892 subsequences decrescendo triangle.

1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 2, 1, 2, 1, 0, 0, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1

Offset: 0

Author

Gary W. Adamson, Sep 10 2008

Keywords

• nonn
• tabl

Comments

n-th row = (n+1) terms of an infinitely periodic cycle: (..., 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1), shifting to the right one place for the next row.

Construct an A010892 decrescendo triangle: (1; 1,1; 0,1,1; -1,0,1,1; ...) and take partial sums starting from the right.

Examples

			First few rows of the triangle:
  1;
  2, 1;
  2, 2, 1;
  1, 2, 2, 1;
  0, 1, 2, 2, 1;
  0, 0, 1, 2, 2, 1;
  1, 0, 0, 1, 2, 2, 1;
  2, 1, 0, 0, 1, 2, 2, 1;
  2, 2, 1, 0, 0, 1, 2, 2, 1;
  1, 2, 2, 1, 0, 0, 1, 2, 2, 1;
  0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1;
  ...
Row 3 = (1, 2, 2, 1) = partial sums of (-1, 0, 1, 1).
		

Crossrefs

Cf. A010892, A077859 (row sums), A164965 (1st column).

Programs

Mathematica

A010892[n_]:={1, 1, 0, -1, -1,0}[[Mod[n, 6]+1]]; T[n_,k_]:=1+A010892[n-k-1]; Table[T[n,k], {n,0, 11},{k,0,n}]//Flatten (* Stefano Spezia, Feb 11 2023 *)

Formula

T(n, k) = 1 + A010892(n-k-1), with 0 <= k <= n. - Stefano Spezia, Feb 11 2023