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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
OFFSET
0,5
COMMENTS
A242105 gives the first nonzero terms per row, without repetitions. - Reinhard Zumkeller, Sep 06 2015
LINKS
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: A104041 A104402 A377069 * A131084 A143067 A219605
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Sep 05 2015
STATUS
approved