OFFSET
0,4
COMMENTS
A Jacobsthal-Pascal triangle.
LINKS
G. C. Greubel, Rows n = 0..20 of triangle, flattened
FORMULA
k-th column has e.g.f. ((1-x)/(1-x-x^2))*(x/(1-x))^k.
EXAMPLE
Triangle starts as:
1;
0, 1;
2, 1, 1;
2, 3, 2, 1;
6, 5, 5, 3, 1;
10, 11, 10, 8, 4, 1;
22, 21, 21, 18, 12, 5, 1;
42, 43, 42, 39, 30, 17, 6, 1; ...
MATHEMATICA
T[n_, k_]:= If[k==0, (2^n + 2*(-1)^n)/3, If[k<0 || k>n, 0, T[n-1, k-1] + T[n-1, k]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 04 2019 *)
PROG
(PARI) {T(n, k) = if(k==0, (2^n + 2*(-1)^n)/3, if(k<0 || k>n, 0, T(n-1, k-1) + T(n-1, k)))}; \\ G. C. Greubel, Jun 04 2019
(Sage)
def T(n, k):
if (k<0 or k>n): return 0
elif (k==0): return (2^n + 2*(-1)^n)/3
else: return T(n-1, k-1) + T(n-1, k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jun 04 2019
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jan 23 2004
STATUS
approved