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A140736 Triangle read by rows, X^n * [1,0,0,0,...]; where X = a tridiagonal matrix with (1,0,1,0,1,...) in the main diagonal and (1,1,1,...) in the sub- and subsubdiagonals. 2
1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 5, 4, 6, 3, 1, 1, 1, 7, 6, 15, 10, 10, 4, 1, 1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1, 1, 1, 11, 10, 45, 36, 84, 56, 70, 35, 21, 6, 1, 1, 1, 13, 12, 66, 55, 165, 120, 210, 126, 126, 56, 28, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row sums = F(2n), where A001906 = (1, 3, 8, 21, 55, ...). Example: Row 4 terms = (1, 1, 5, 4, 6, 3, 1), sum = 21 = F(8).

The presence of the terms in Pascal's triangle points to a combinatorial version.

A140737 = triangle with reversed terms by rows. - Gary W. Adamson, May 25 2008

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

First few rows of the triangle are:

  1;

  1, 1,  1;

  1, 1,  3,  2,  1;

  1, 1,  5,  4,  6,  3,   1;

  1, 1,  7,  6, 15, 10,  10,   4,   1;

  1, 1,  9,  8, 28, 21,  35,  20,  15,   5,   1;

  1, 1, 11, 20, 45, 36,  84,  56,  70,  35,  21,  6,  1;

  1, 1, 13, 12, 66, 55, 165, 120, 210, 126, 126, 56, 28, 7, 1;

  ...

CROSSREFS

Cf. A001906.

Cf. A140737.

Sequence in context: A257657 A106689 A027082 * A284993 A292068 A140056

Adjacent sequences:  A140733 A140734 A140735 * A140737 A140738 A140739

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson and Roger L. Bagula, May 25 2008

STATUS

approved

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Last modified February 21 00:32 EST 2018. Contains 299388 sequences. (Running on oeis4.)