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

0,6

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.

Links

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

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

Example

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).

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_] /; 0<k<n := row[n][[k+1]];
Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 07 2018 *)

Crossrefs

Cf. A001006, A086246.

Sequence in context: A232084 A261359 A217680 * A098691 A324251 A035364

Adjacent sequences: A144215 A144216 A144217 * A144219 A144220 A144221

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 14 2008

Extensions

Edited by Joerg Arndt, Jan 26 2024

Status

approved