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A279009
Alternating Jacobsthal triangle A_{-2}(n,k) read by rows.
3
1, 1, 1, -2, 0, 1, -2, -2, -1, 1, 4, 0, -1, -2, 1, 4, 4, 1, 1, -3, 1, -8, 0, 3, 0, 4, -4, 1, -8, -8, -3, 3, -4, 8, -5, 1, 16, 0, -5, -6, 7, -12, 13, -6, 1, 16, 16, 5, 1, -13, 19, -25, 19, -7, 1, -32, 0, 11, 4, 14, -32, 44, -44, 26, -8, 1
OFFSET
0,4
LINKS
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
EXAMPLE
Triangle begins:
1,
1, 1,
-2, 0, 1,
-2, -2, -1, 1,
4, 0, -1, -2, 1,
4, 4, 1, 1, -3, 1,
-8, 0, 3, 0, 4, - 4, 1,
-8, -8, -3, 3, -4, 8, -5, 1,
16, 0, -5, -6, 7, -12, 13, -6, 1,
16, 16, 5, 1, -13, 19, -25, 19, -7, 1,
-32, 0, 11, 4, 14, -32, 44, -44, 26, -8, 1,
...
MATHEMATICA
a[n_, 0] := (-2)^Floor[n/2]; a[n_, n_] = 1; a[n_, k_] /; 0 <= k <= n := a[n, k] = a[n-1, k-1] - a[n-1, k]; a[_, _] = 0;
Table[a[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Oct 05 2018 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
N. J. A. Sloane, Dec 07 2016
STATUS
approved