

A144218


Eigentriangle, row sums and borders = offset variations of Motzkin numbers


3



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
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OFFSET

0,6


COMMENTS

Right border = Motzkin numbers, A001006: (1, 1, 2, 4, 9, 21,...).
Row sums = (1, 2, 4, 9, 21,...);
Left border = A086246: (1, 1, 1, 2, 4, 9, 21,...).Q Sum of nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=0..65.
P. Barry, Invariant number triangles, eigentriangles and Somos4 sequences, arXiv preprint arXiv:1107.5490, 2011


FORMULA

Let A = an infinite lower triangular matrix with A086246: (1, 1, 1, 2, 4, 9, 21, 51,...) in every column; and B = an infinite lower triangular matrix with A001006, (1, 1, 2, 4, 9, 21,...) as the main diagonal and the rest zeros.
a144218 = A*B.


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, 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).


CROSSREFS

A001006, Cf. A086246
Sequence in context: A048299 A232084 A217680 * A098691 A035364 A209308
Adjacent sequences: A144215 A144216 A144217 * A144219 A144220 A144221


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Sep 14 2008


STATUS

approved



