A030506 Graham-Sloane-type lower bound on the size of a ternary (n,3,6) constant-weight code.

5, 30, 106, 283, 640, 1286, 2366, 4068, 6628, 10333, 15531, 22631, 32111, 44525, 60504, 80766, 106117, 137460, 175799, 222244, 278014, 344448, 423007, 515276, 622978, 747968, 892251, 1057976, 1247448, 1463131, 1707654, 1983816, 2294592, 2643138, 3032795, 3467095

Offset

6,1

Links

Table of n, a(n) for n=6..41.

Mattias Svanstrom, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43 (Sep. 1997), pp. 1630-1632.

Formula

a(n) = ceiling(binomial(n, w) * 2^w / (2*n + 1)) with w = 6.

If n is in {1,2,3,4,5,10,27,31,38,577}, then a(n) = binomial(n, 6) * 64 / (2*n + 1). Otherwise, a(n) = 1 + floor(binomial(n, 6) * 64 / (2*n + 1)). - Chai Wah Wu, May 12 2026

Mathematica

a[n_] := Ceiling[Binomial[n, 6] * 2^6 / (2*n + 1)]; Array[a, 40, 6] (* Amiram Eldar, Oct 31 2025 *)

Prog

(Python)
from math import comb
def A030506(n):
    a, b = divmod(comb(n, 6)<<6, (n<<1|1))
    return a+bool(b) # Chai Wah Wu, May 12 2026

Crossrefs

Column k=6 of A390161.

Sequence in context: A288679 A071252 A174002 * A062990 A018213 A359975

Adjacent sequences: A030503 A030504 A030505 * A030507 A030508 A030509

Keyword

nonn,easy

Author

Mattias Svanstrom (mattias(AT)isy.liu.se)

Status

approved