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A204293
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Pascal's triangle interspersed with rows of zeros, and the rows of Pascal's triangle are interspersed with zeros.
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5
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1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 6, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 10, 0, 10, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 0, 15, 0, 20
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OFFSET
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0,13
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COMMENTS
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Auxiliary array for computing Losanitsch's triangle A034851;
T(n, k) + T(n, k + 2) = T(n + 2, k + 2) for k < n - 1.
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LINKS
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_Reinhard Zumkeller_, Rows n=0..100 of triangle, flattened
N. J. A. Sloane, Classic Sequences: Losanitsch's Triangle
Eric Weisstein's World of Mathematics, Losanitsch's Triangle
Index entries for triangles and arrays related to Pascal's triangle
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FORMULA
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T(n, k) = (1 - n mod 2) * (1 - k mod 2) * A007318((n+2)/2-1, (k-1)/2).
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MATHEMATICA
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t[n_?EvenQ, k_?EvenQ] := Binomial[n/2, k/2]; t[_, _] = 0; Flatten[Table[t[n, k], {n, 0, 12}, {k, 0, n}]] (* From Jean-François Alcover, Feb 07 2012 *)
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PROG
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(Haskell)
a204293 n k = a204293_tabl !! n !! k
a204293_row n = a204293_tabl !! n
a204293_tabl = [1] : [0, 0] : f [1] [0, 0] where
f xs ys = xs' : f ys xs' where
xs' = zipWith (+) ([0, 0] ++ xs) (xs ++ [0, 0])
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CROSSREFS
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Cf. A077957 (row sums), A126869 (central terms); A108044, A007318.
Sequence in context: A064530 A037047 A118917 * A206479 A219484 A060396
Adjacent sequences: A204290 A204291 A204292 * A204294 A204295 A204296
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller, Jan 14 2012
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STATUS
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approved
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