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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A232084 A261359 A217680 * A098691 A324251 A035364
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Sep 14 2008
EXTENSIONS
Edited by Joerg Arndt, Jan 26 2024
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)