A140750 - OEIS

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A140750

Triangle read by rows, X^n * [1,0,0,0,...]; where X = an infinite tridiagonal matrix with (1,0,1,0,1,...) in the main and subsubdiagonals and (1,1,1,...) in the subdiagonal.

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 3, 5, 1, 1, 1, 1, 7, 5, 13, 5, 7, 1, 1, 1, 1, 9, 7, 25, 13, 25, 7, 9, 1, 1, 1, 1, 11, 9, 41, 25, 63, 25, 41, 9, 11, 1, 1, 1, 1, 13, 11, 61, 41, 129, 63, 129, 41, 61, 11, 13, 1, 1

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OFFSET

1,7

COMMENTS

Row sums = A001333 starting (1, 3, 7, 17, 41, 99, 239,...).

Can also be seen as a triangle where each entry is the sum of two terms above it in previous row (as in Pascal's triangle) plus one term above it two rows back, see also A059317. - Reinhard Zumkeller, Jun 30 2012

LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

S. Samieinia, The number of continuous curves in digital geometry, Port. Math. 67 (1) (2010) 75-89

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

First few rows of the triangle are:

1, 1, 1;

1, 1, 3, 1, 1;

1, 1, 5, 3, 5, 1, 1;

1, 1, 7, 5, 13, 5, 7, 1, 1;

1, 1, 9, 7, 25, 13, 25, 7, 9, 1, 1;

1, 1, 11, 9, 41, 25, 63, 25, 41, 9, 11, 1, 1;