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

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, 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 !! (n-1) !! (k-1)
a140750_row n = a140750_tabf !! (n-1)
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