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A342138
Array T(n,k) = (n+k)*(3*n+3*k-5)/2 + (3*k+1), read by ascending antidiagonals.
0
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
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
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Mar 01 2021
STATUS
approved