A279010 Alternating Jacobsthal triangle A_3(n,k) read by rows.

1, 1, 1, 3, 0, 1, 3, 3, -1, 1, 9, 0, 4, -2, 1, 9, 9, -4, 6, -3, 1, 27, 0, 13, -10, 9, -4, 1, 27, 27, -13, 23, -19, 13, -5, 1, 81, 0, 40, -36, 42, -32, 18, -6, 1, 81, 81, -40, 76, -78, 74, -50, 24, -7, 1, 243, 0, 121, -116, 154, -152, 124, -74, 31, -8, 1

Offset: 0

Author

N. J. A. Sloane, Dec 07 2016

Keywords

• sign
• tabl

Examples

			Triangle begins:
    1;
    1,  1;
    3,  0,   1;
    3,  3,  -1,    1;
    9,  0,   4,   -2,   1;
    9,  9,  -4,    6,  -3,    1;
   27,  0,  13,  -10,   9,   -4,   1;
   27, 27, -13,   23, -19,   13,  -5,   1;
   81,  0,  40,  -36,  42,  -32,  18,  -6,  1;
   81, 81, -40,   76, -78,   74, -50,  24, -7,  1;
  243,  0, 121, -116, 154, -152, 124, -74, 31, -8, 1;
  ...
		

Links

• Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.

Crossrefs

If initial column is omitted, this is very like the Riordan matrix A191582.

Cf. A112468, A279006, A279009.

Programs

Mathematica

A[n_, 0] := 3^Floor[n/2];
A[n_, k_] /; (k<0 || t>n) = 0;
A[n_, n_] = 1;
A[n_, k_] := A[n, k] = A[n-1, k-1] - A[n-1, k];
Table[A[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 12 2018 *)