A219463 Triangle read by rows: T(n,k) = 1 - A047999(n,k), 0 <= k <= n.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1

Offset

0

Comments

Sierpinski's triangle complemented.

Links

Reinhard Zumkeller, Rows n = 0..128 of triangle, flattened

Eric Weisstein's World of Mathematics, Sierpinski Sieve

Wikipedia, Sierpinski triangle

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(n,k) = if T(n-1,k-1) = T(n-1,k) then 1 else 0, 0 < k < n.

Example

The triangle begins:
   0:                 0
   1:                0 0
   2:               0 1 0
   3:              0 0 0 0
   4:             0 1 1 1 0
   5:            0 0 1 1 0 0
   6:           0 1 0 1 0 1 0
   7:          0 0 0 0 0 0 0 0
   8:         0 1 1 1 1 1 1 1 0
   9:        0 0 1 1 1 1 1 1 0 0
  10:       0 1 0 1 1 1 1 1 0 1 0
  11:      0 0 0 0 1 1 1 1 0 0 0 0
  12:     0 1 1 1 0 1 1 1 0 1 1 1 0
  13:    0 0 1 1 0 0 1 1 0 0 1 1 0 0
  14:   0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
  15:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Mathematica

A219463row[n_]:=Sign[BitAnd[Range[0, n], -1-n]]; Array[A219463row, 20, 0] (* Paolo Xausa, May 22 2023 *)

Prog

(Haskell)
a219463 n k = a219463_tabl !! n !! k :: Int
a219463_row n = a219463_tabl !! n
a219463_tabl = map (map (1 -)) a047999_tabl
(PARI) T(n, k)= bitand(n-k, k) != 0;  \\ Joerg Arndt, May 22 2023

Crossrefs

Cf. A000004 (left and right edges), A057427 (central terms), A048967 (row sums = number of ones per row), A001316 (number of zeros per row), A219843 (rows as binary numbers).

Sequence in context: A354035 A025457 A350289 * A286688 A356923 A356924

Adjacent sequences: A219460 A219461 A219462 * A219464 A219465 A219466

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Nov 30 2012

Status

approved