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

0,4

Links

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

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)

Example

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;

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 *)

Prog

(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

Crossrefs

Cf. A000027, A109613, A145677.

Sequence in context: A309576 A128132 A127701 * A004199 A062283 A136493

Adjacent sequences: A158818 A158819 A158820 * A158822 A158823 A158824

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Mar 30 2008

Status

approved