OFFSET
0,4
COMMENTS
From Paul Curtz, Nov 12 2019: (Start)
If a new main diagonal of 0's is added to the triangle, then for this variant the following propositions hold:
The first column is A166444.
The second column is A139756.
The antidiagonal sums are A000129 (Pell numbers).
The row sums are (-1)^n*A141413.
The signed row sums are 0 followed by 1's, autosequence companion to A054977.
(End)
FORMULA
EXAMPLE
Triangle begins:
1;
1, 0;
2, 1, 0;
4, 4, 1, 0;
8, 12, 6, 1, 0;
16, 32, 24, 8, 1, 0;
32, 80, 80, 40, 10, 1, 0;
...
MAPLE
T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
`if`(n<2, 1-k, 2*T(n-1, k) +T(n-1, k-1)))
end:
seq(seq(T(n, k), k=0..n), n=0..12); # Alois P. Heinz, Nov 08 2019
MATHEMATICA
T[n_, k_] /; 0 <= k <= n := T[n, k] = 2 T[n-1, k] + T[n-1, k-1];
T[0, 0] = T[1, 0] = 1; T[1, 1] = 0; T[_, _] = 0;
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 08 2019 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Dec 14 2011
STATUS
approved