A342138 Array T(n,k) = (n+k)*(3*n+3*k-5)/2 + (3*k+1), read by ascending antidiagonals.

1, 0, 3, 2, 5, 8, 7, 10, 13, 16, 15, 18, 21, 24, 27, 26, 29, 32, 35, 38, 41, 40, 43, 46, 49, 52, 55, 58, 57, 60, 63, 66, 69, 72, 75, 78, 77, 80, 83, 86, 89, 92, 95, 98, 101, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156

Offset: 0

Author

Michel Marcus, Mar 01 2021

Keywords

• nonn
• tabl

Comments

This is an instance of a storing function on N^2 (injective) with density 1/3.

Examples

			Array begins:
   1  3   8  16  27 ...
   0  5  13  24  38 ...
   2 10  21  35  52 ...
   7 18  32  49  69 ...
  15 29  46  66  89 ...
  ...
		

Links

• John S. Lew and Arnold L. Rosenberg, Polynomial indexing of integer lattice-points I. General concepts and quadratic polynomials, Journal of Number Theory, 10(2):215-243, 1978. See Corollary 5.2 p. 211.

Crossrefs

Cf. A005449 (first column), A104249 (first row), A140090 (second row), A201279 (diagonal).

Programs

PARI

T(n,k) = (n+k)*(3*n+3*k-5)/2 + (3*k+1);
matrix(8, 8, n, k, T(n-1, k-1))