A253084 Triangle read by rows: T(n,k) = {binomial(n+k,n-k)*binomial(n,k)} mod 2, 0 <= k <= n.

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

Offset

0

Comments

Row sums give A106737.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10010

Formula

T(n,k) = 1 if and only if ((n-k) AND NOT (n+k)) OR (k AND NOT n) is zero where AND, OR and NOT are bitwise operators. - Chai Wah Wu, Feb 09 2016

Example

Triangle begins:
[1]
[1, 1]
[1, 0, 1]
[1, 0, 1, 1]
[1, 0, 0, 0, 1]
[1, 1, 0, 0, 1, 1]
[1, 0, 0, 0, 1, 0, 1]
[1, 0, 0, 0, 1, 0, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 0, 1]
[1, 1, 0, 0, 0, 0, 0, 0, 1, 1]
[1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]
[1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]
[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
...

Mathematica

Table[Mod[Binomial[n + k, n - k] Binomial[n, k], 2], {n, 0, 13}, {k, 0, n}] // Flatten (* Michael De Vlieger, Feb 10 2016 *)

Prog

(PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1((binomial(n+k, n-k)*binomial(n, k)) % 2, ", "); ); print(); ); } \\ Michel Marcus, Feb 06 2015
(Python)
def A253084_T(n, k):
    return int(not (~(n+k) & (n-k)) | (~n & k)) # Chai Wah Wu, Feb 09 2016
(Magma) /* As triangle */ [[Binomial(n+k, n-k)*Binomial(n, k) mod 2: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Feb 10 2016

Crossrefs

Cf. A082759, A106737.

Sequence in context: A343910 A329682 A113998 * A182741 A070909 A115954

Adjacent sequences: A253081 A253082 A253083 * A253085 A253086 A253087

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 05 2015

Status

approved