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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

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.

EXAMPLE

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,

...

PROG

(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

CROSSREFS

Cf. A242105, A261930 (row sums).

Sequence in context: A051070 A104041 A104402 * A131084 A143067 A219605

Adjacent sequences:  A261894 A261895 A261896 * A261898 A261899 A261900

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Sep 05 2015

STATUS

approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)