A249133 Triangle read by rows: interleaving successive pairs of rows of Sierpiński's triangle.

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

Offset

0

Comments

A105321(n) = number of ones in row n;

A249304(n) = number of zeros in row n;

numbers, when rows are concatenated: A249183, A249184.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10200

Formula

T(n,k) = A249095(n,k) mod 2.

Example

.   0:                                 1
.   1:                               1 1 1
.   2:                             1 1 0 1 1
.   3:                           1 1 1 0 1 1 1
.   4:                         1 1 0 1 0 1 0 1 1
.   5:                       1 1 1 0 0 0 0 0 1 1 1
.   6:                     1 1 0 1 1 0 0 0 1 1 0 1 1
.   7:                   1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
.   8:                 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1
.   9:               1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
.  10:             1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
.  11:           1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1
.  12:         1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1
.  13:       1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1
.  14:     1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1
.  15:   1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
.  16: 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 .

Mathematica

row[n_] := Mod[Riffle[Binomial[n, Range[0, n]], Binomial[n - 1, Range[0, n - 1]]], 2]; Table[row[n], {n, 0, 10}] // Flatten (* Amiram Eldar, Jul 28 2023 *)

Prog

(Haskell)
a249133 n k = a249133_tabf !! n !! k
a249133_row n = a249133_tabf !! n
a249133_tabf = map (map (flip mod 2)) a249095_tabf

Crossrefs

Cf. A005408 (row lengths), A105321 (row sums), A249095, A249304, A249183, A249184, A047999 (Sierpiński).

Sequence in context: A303300 A249865 A152904 * A118102 A089509 A157972

Adjacent sequences: A249130 A249131 A249132 * A249134 A249135 A249136

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Nov 14 2014

Status

approved