A346619 Triangle read by rows: T(n,k) = 1 iff 4 divides binomial(n,k) but 8 does not (0 <= k <= n).

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

Offset

0

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

P. Goetgheluck, Computing binomial coefficients, The American Mathematical Monthly 94.4 (1987): 360-365. See Fig. 3.

Example

Triangle begins:
0,
0, 0,
0, 0, 0,
0, 0, 0, 0,
0, 1, 0, 1, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 1, 0, 0,
0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0,
0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
...

Mathematica

Table[With[{c=Binomial[n, k]}, If[Mod[c, 4]==0&&Mod[c, 8]!=0, 1, 0]], {n, 0, 20}, {k, 0, n}]//Flatten (* Harvey P. Dale, Aug 22 2025 *)

Crossrefs

Cf. A007318, A007814, A047999, A346618.

Sequence in context: A353798 A193095 A011725 * A037808 A023973 A297040

Adjacent sequences: A346616 A346617 A346618 * A346620 A346621 A346622

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 21 2021

Status

approved