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
KEYWORD
AUTHOR
Gary W. Adamson, Mar 30 2008
STATUS
approved