A342384 Irregular triangle T read by rows: T(n, k) is the number of n-th order magic triangles with magic constant equal to A285009(n) + k, with 0 < k <= 3*n - 5.

0, 1, 1, 1, 1, 2, 0, 4, 6, 4, 0, 2, 18, 38, 71, 108, 115, 115, 108, 71, 38, 18, 155, 351, 695, 1067, 1475, 1815, 2007, 1815, 1475, 1067, 695, 351, 155, 1891, 4768, 9872, 15370, 22527, 30096, 35731, 37957, 37957, 35731, 30096, 22527, 15370, 9872, 4768, 1891

Offset

2,6

Links

Andrew Howroyd, Table of n, a(n) for n = 2..118 (rows 2..10)

Terrel Trotter, Normal Magic Triangles of Order n, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.

Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20.

Example

The triangle begins:
    0;
    1,   1,   1,    1;
    2,   0,   4,    6,    4,    0,    2;
   18,  38,  71,  108,  115,  115,  108,   71,   38,   18;
  155, 351, 695, 1067, 1475, 1815, 2007, 1815, 1475, 1067, 695, 351, 155;
  ...

Prog

(PARI) \\ See A342467 for program code.
{ for(n=2, 6, print(A342384row(n))) } \\ Andrew Howroyd, Feb 05 2022

Crossrefs

Cf. A016777 (row length), A179805, A285009, A341740, A342467 (row sums).

Sequence in context: A192133 A244109 A133144 * A192134 A322402 A196877

Adjacent sequences: A342381 A342382 A342383 * A342385 A342386 A342387

Keyword

nonn,tabf

Author

Stefano Spezia, Mar 10 2021

Extensions

Terms a(14) and beyond from Andrew Howroyd, Feb 05 2022

Status

approved