OFFSET
0,14
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n,k) = T(n-1,k-1) - T(n-2,k-1), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
Sum_{k=0..n} T(n, k) = A057079(n).
EXAMPLE
Triangles begins:
1;
1, 1;
0, 0, 1;
0, -1, -1, 1;
0, 0, -1, -2, 1;
0, 0, 1, 0, -3, 1;
0, 0, 0, 2, 2, -4, 1;
0, 0, 0, -1, 2, 5, -5, 1;
0, 0, 0, 0, -3, 0, 9, -6, 1;
0, 0, 0, 0, 1, -5, -5, 14, -7, 1;
...
Production matrix is:
1, 1;
-1, -1, 1;
0, -1, -1, 1;
-1, -2, -1, -1, 1;
-2, -5, -2, -1, -1, 1;
-6, -14, -5, -2, -1, -1, 1;
-18, -42, -14, -5, -2, -1, -1, 1;
-57, -132, -42, -14, -5, -2, -1, -1, 1;
-186, -429, -132, -42, -14, -5, -2, -1, -1, 1;
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n<2, 1, T[n-1, k-1] - T[n-2, k-1] ]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, May 26 2022 *)
PROG
(SageMath)
def T(n, k): # T = A237621
if (k<0 or k>n): return 0
elif (n<2): return 1
else: return T(n-1, k-1) - T(n-2, k-1)
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 26 2022
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Philippe Deléham, Feb 10 2014
STATUS
approved