A204293 - OEIS

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A204293

Pascal's triangle interspersed with rows of zeros, and the rows of Pascal's triangle are interspersed with zeros.

6

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

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

OFFSET

0,13

COMMENTS

Auxiliary array for computing Losanitsch's triangle A034851;

T(n, k) + T(n, k + 2) = T(n + 2, k + 2) for k < n - 1.

LINKS

Reinhard Zumkeller, Rows n=0..100 of triangle, flattened

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)

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

FORMULA

T(n, k) = (1 - n mod 2) * (1 - k mod 2) * binomial(floor(n/2),floor(k/2)).

MATHEMATICA

t[n_?EvenQ, k_?EvenQ] := Binomial[n/2, k/2]; t[_, _] = 0; Flatten[Table[t[n, k], {n, 0, 12}, {k, 0, n}]] (* Jean-François Alcover, Feb 07 2012 *)

PROG

(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])

CROSSREFS

Cf. A077957 (row sums), A126869 (central terms); A108044, A007318.

Sequence in context: A037047 A118917 A325045 * A206479 A219484 A060396

Adjacent sequences: A204290 A204291 A204292 * A204294 A204295 A204296

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jan 14 2012

EXTENSIONS

Formula for T(n,k) corrected by Peter Bala, Jul 06 2015

STATUS

approved