A144218 Equals product A*B, where A is an infinite lower triangular matrix with A086246 in every column and B is the diagonal matrix with A001006 as diagonal.

1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 4, 2, 2, 4, 9, 9, 4, 4, 4, 9, 21, 21, 9, 8, 8, 9, 21, 51, 51, 21, 18, 16, 18, 21, 51, 127, 127, 51, 42, 36, 36, 42, 51, 127, 323, 323, 127, 102, 84, 81, 84, 102, 127, 323, 835, 835, 323, 254, 204, 189, 189, 204, 254, 323, 835, 2188

Offset: 0

Author

Gary W. Adamson, Sep 14 2008

Keywords

• nonn
• tabl

Comments

Right border is A001006.

Row sums give A001006 without the initial 1.

Left border is A086246 (A001006 with an additional leading 1).

Sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle:
    1;
    1,   1;
    1,   1,   2;
    2,   1,   2,   4;
    4,   2,   2,   4,   9;
    9,   4,   4,   4,   9,  21;
   21,   9,   8,   8,   9,  21,  51;
   51,  21,  18,  16,  18,  21,  51, 127;
  127,  51,  42,  36,  36,  42,  51, 127, 323;
  323, 127, 102,  84,  81,  84, 102, 127, 323, 835;
  835, 323, 254, 204, 189, 189, 204, 254, 323, 835, 2188;
  ...
Row 4 = (4, 2, 2, 4, 9) = termwise products of (4, 2, 1, 1, 1) and (1, 1, 2, 4, 9) = (4*1, 2*1, 1*2, 1*4, 1*9).
		

Links

• Paul Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490 [math.CO], 2011.

Crossrefs

Cf. A001006, A086246.

Programs

Mathematica

nmax = 10;
T[0, 0] = T[1, 0] = 1;
T[n_, 0]  := Hypergeometric2F1[3/2, 1-n, 3, 4] // Abs;
T[n_, n_] := Hypergeometric2F1[(1-n)/2, -n/2, 2, 4];
row[n_] := row[n] = Table[T[m, 0], {m, n, 0, -1}]*Table[T[m, m], {m, 0, n} ];
T[n_, k_] /; 0Jean-François Alcover, Aug 07 2018 *)

Extensions

Edited by Joerg Arndt, Jan 26 2024