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A030503 Graham-Sloane-type lower bound on the size of a ternary (n,3,3) constant-weight code. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
LINKS
M. Svanstrom, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43, pp. 1630-1632, Sep. 1997.
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
KEYWORD
nonn
AUTHOR
Mattias Svanstrom (mattias(AT)isy.liu.se)
STATUS
approved

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Last modified April 12 20:38 EDT 2024. Contains 371639 sequences. (Running on oeis4.)