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%I #19 Sep 02 2023 10:35:03
%S 1,1,2,2,3,6,9,16,29,51,93,172,315,585,1094,2048,3855,7285,13797,
%T 26214,49938,95325,182361,349536,671088,1290555,2485532,4793490,
%U 9256395,17895730,34636833,67108864,130150586,252645135,490853403
%N 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).
%D 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.
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/dijen.txt">On single-deletion-correcting codes</a>
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/dijen.pdf">On single-deletion-correcting codes</a>, 2002.
%e From _Seiichi Manyama_, Sep 02 2023: (Start)
%e 1 + 2 == 3 mod 6,
%e 3 == 3 mod 6,
%e 1 + 3 + 5 == 3 mod 6,
%e 2 + 3 + 4 == 3 mod 6,
%e 4 + 5 == 3 mod 6,
%e 1 + 2 + 3 + 4 + 5 == 3 mod 6.
%e So a(5) = 6. (End)
%o (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
%Y For the codes VT_0(n), VT_1(n), VT_2(n) see resp. A000016, A000048, A000048 (again).
%Y Cf. A000010, A008683, A053633.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 29 2000
%E Offset changed to 0 by _Seiichi Manyama_, Sep 02 2023
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