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

0,3

Comments

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

Links

Table of n, a(n) for n=0..65.

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.

Example

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 ...
  ...

Prog

(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))

Crossrefs

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

Sequence in context: A019594 A085167 A127299 * A029619 A049922 A160106

Adjacent sequences: A342135 A342136 A342137 * A342139 A342140 A342141

Keyword

nonn,tabl

Author

Michel Marcus, Mar 01 2021

Status

approved