A158821 Triangle read by rows: row n (n>=0) ends with 1, and for n>=1 begins with n; other entries are zero.

1, 1, 1, 2, 0, 1, 3, 0, 0, 1, 4, 0, 0, 0, 1, 5, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 1, 7, 0, 0, 0, 0, 0, 0, 1, 8, 0, 0, 0, 0, 0, 0, 0, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Gary W. Adamson, Mar 30 2008

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1;
  1, 1;
  2, 0, 1;
  3, 0, 0, 1;
  4, 0, 0, 0, 1;
  5, 0, 0, 0, 0, 1;
  6, 0, 0, 0, 0, 0, 1;
  7, 0, 0, 0, 0, 0, 0, 1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A000027, A109613, A145677.

Programs

Maple

A158821:= proc(n,k)
    if n = k then 1;
    elif k = 0 then n;
    else 0;
    end if;
end proc: # R. J. Mathar, Jan 08 2015

Mathematica

T[n_, k_]:= If[k==0, Boole[n==0] +n, If[k==n, 1, 0]];
Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Dec 22 2021 *)
Join[{1},Table[Join[{n},PadLeft[{1},n,0]],{n,15}]]//Flatten (* Harvey P. Dale, Apr 05 2023 *)

Sage

def A158821(n,k):
    if (k==0): return n + bool(n==0)
    elif (k==n): return 1
    else: return 0
flatten([[A158821(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Dec 22 2021

Formula

T(n, k) = A145677(n, n-k-1). - R. J. Mathar, Apr 01 2009

From G. C. Greubel, Dec 22 2021: (Start)

Sum_{k=0..n} T(n, k) = A000027(n).

Sum_{k=0..floor(n/2)} T(n-k, k) = A109613(n). (End)