

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.


4



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) 7589
Index entries for triangles and arrays related to Pascal's triangle


EXAMPLE

First few rows of the triangle are:
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;
...


PROG

(Haskell)
a140750 n k = a140750_tabf !! (n1) !! (k1)
a140750_row n = a140750_tabf !! (n1)
a140750_tabf = [1] : [1, 1, 1] : f [1] [1, 1, 1] where
f ws vs = vs' : f vs vs' where
vs' = zipWith3 (\r s x > r + s + x)
(vs ++ [0, 0]) ([0, 0] ++ ws ++ [0, 0]) ([0, 0] ++ vs)
 Reinhard Zumkeller, Jun 30 2012


CROSSREFS

Cf. A001333, A140751.
Cf. A005408 (row lengths).
Sequence in context: A079724 A289357 A111368 * A028264 A208673 A010122
Adjacent sequences: A140747 A140748 A140749 * A140751 A140752 A140753


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson & Roger L. Bagula, May 26 2008


STATUS

approved



