A054200 Number of binary vectors (x_1,...x_n) satisfying Sum_{i=1..n} i*x_i = 3 (mod n+1) = size of Varshamov-Tenengolts code VT_3(n).

1, 1, 2, 2, 3, 6, 9, 16, 29, 51, 93, 172, 315, 585, 1094, 2048, 3855, 7285, 13797, 26214, 49938, 95325, 182361, 349536, 671088, 1290555, 2485532, 4793490, 9256395, 17895730, 34636833, 67108864, 130150586, 252645135, 490853403

Offset: 0

Author

N. J. A. Sloane, Apr 29 2000

Keywords

• nonn

Examples

			From _Seiichi Manyama_, Sep 02 2023: (Start)
1 + 2 == 3 mod 6,
3 == 3 mod 6,
1 + 3 + 5 == 3 mod 6,
2 + 3 + 4 == 3 mod 6,
4 + 5 == 3 mod 6,
1 + 2 + 3 + 4 + 5 == 3 mod 6.
So a(5) = 6. (End)
		

References

• N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

Links

• N. J. A. Sloane, On single-deletion-correcting codes
• N. J. A. Sloane, On single-deletion-correcting codes, 2002.

Crossrefs

For the codes VT_0(n), VT_1(n), VT_2(n) see resp. A000016, A000048, A000048 (again).

Cf. A000010, A008683, A053633.

Programs

PARI

a(n, k=3) = sumdiv(n+1, d, (d%2)*eulerphi(d)*moebius(d/gcd(d, k))/eulerphi(d/gcd(d, k))*2^((n+1)/d))/(2*(n+1)); \\ Seiichi Manyama, Sep 02 2023

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 02 2023