A257564 Irregular triangle read by rows: T(n,k) = r(n+k)+r(n-k) with r(n) = (n-(n mod 2))/2 for n>=0 and -n<=k<=n.

0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8

Offset: 0

Author

Peter Luschny, May 28 2015

Keywords

• tabf
• easy
• nonn

Comments

r(n+k)-r(n-k) is triangle A196199(n,k).

Examples

			Triangle starts:
                 0;
              1, 0, 1;
           2, 1, 2, 1, 2;
        3, 2, 3, 2, 3, 2, 3;
     4, 3, 4, 3, 4, 3, 4, 3, 4;
  5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5;
		

Crossrefs

Cf. A001105, A196199, A253580.

Programs

Maple

r := n -> (n-(n mod 2))/2: T := (n,k) -> r(n+k) + r(n-k):
seq(print(seq(T(n,k), k=-n..n)), n=0..6);

Sage

for n in (0..6):
    [(n+k)//2 + (n-k)//2 for k in (-n..n)]

Formula

Sum_{k=-n..n} T(n,k) = 2*n^2 = A001105(n).