A030503 Graham-Sloane-type lower bound on the size of a ternary (n,3,3) constant-weight code.

2, 4, 8, 13, 19, 27, 36, 46, 58, 71, 85, 101, 118, 136, 156, 177, 199, 223, 248, 274, 302, 331, 361, 393, 426, 460, 496, 533, 571, 611, 652, 694, 738, 783, 829, 877, 926, 976, 1028, 1081, 1135, 1191, 1248, 1306, 1366, 1427, 1489, 1553, 1618

Offset

3,1

Links

Robert Israel, Table of n, a(n) for n = 3..10000

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

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

a(n) = ceiling(binomial(n, w) * 2^w / (2*n + 1)) with w=3.

Conjectures from Colin Barker, Aug 02 2019: (Start)

G.f.: x^3*(2 + 2*x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>7.

(End)

From Robert Israel, Jul 09 2020: (Start)

Conjectures confirmed.

a(n) = (2*n^2-7*n+8)/3 if n == 1 (mod 3), otherwise a(n) = (2*n^2-7*n+9)/3.

(End)

Maple

g:= n -> (2*n^2-7*n+`if`(n mod 3 = 1, 8, 9))/3:
map(g, [$3..100]); # Robert Israel, Jul 09 2020

Crossrefs

Sequence in context: A328005 A186752 A360512 * A245094 A164486 A084684

Adjacent sequences: A030500 A030501 A030502 * A030504 A030505 A030506

Keyword

nonn

Author

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

Status

approved