A261897 Triangle read by rows: T(n,k) (1 <= k <= n+1) = number of sequences of length n, dominated by the squares, with entries from [0,k] and largest entry k.

1, 1, 1, 0, 2, 1, 0, 2, 3, 1, 0, 2, 5, 4, 1, 0, 0, 7, 9, 5, 1, 0, 0, 7, 16, 14, 6, 1, 0, 0, 7, 23, 30, 20, 7, 1, 0, 0, 7, 30, 53, 50, 27, 8, 1, 0, 0, 7, 37, 83, 103, 77, 35, 9, 1, 0, 0, 0, 44, 120, 186, 180, 112, 44, 10, 1, 0, 0, 0, 44, 164, 306, 366, 292, 156, 54, 11, 1

Offset: 0

Author

N. J. A. Sloane, Sep 05 2015

Keywords

• nonn
• tabl

Comments

A242105 gives the first nonzero terms per row, without repetitions. - Reinhard Zumkeller, Sep 06 2015

Examples

			Triangle begins:
1,
1,1,
0,2,1,
0,2,3,1,
0,2,5,4,1,
0,0,7,9,5,1,
0,0,7,16,14,6,1,
0,0,7,23,30,20,7,1,
0,0,7,30,53,50,27,8,1,
0,0,7,37,83,103,77,35,9,1,
0,0,0,44,120,186,180,112,44,10,1,
0,0,0,44,164,306,366,292,156,54,11,1,
...
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
• L. Haddad and C. Helou, Finite Sequences Dominated by the Squares, Journal of Integer Sequences, Volume 18, 2015, Issue 1, Article 15.1.8.

Crossrefs

Cf. A242105, A261930 (row sums).

Programs

Haskell

a261897 n k = a261897_tabl !! n !! (k-1)
a261897_row n = a261897_tabl !! n
a261897_tabl = [1] : f 1 0 [1] where
   f t h xs | t <= (h + 1) ^ 2  = ys : f (t + 1) h ys
            | otherwise         = ys' : f (t + 1) (h + 1) ys'
            where ys = zipWith (+) ([0] ++ xs) (xs ++ [0])
                  ys' = zipWith (+) ([0] ++ xs) (us ++ (0:vs) ++ [0])
                  (us, _:vs) = splitAt h xs
-- Reinhard Zumkeller, Sep 06 2015