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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. 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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 02:45 EDT 2018. Contains 316252 sequences. (Running on oeis4.)