cp's OEIS Frontend

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).

%I A054200 #19 Sep 02 2023 10:35:03
%S A054200 1,1,2,2,3,6,9,16,29,51,93,172,315,585,1094,2048,3855,7285,13797,
%T A054200 26214,49938,95325,182361,349536,671088,1290555,2485532,4793490,
%U A054200 9256395,17895730,34636833,67108864,130150586,252645135,490853403
%N 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).
%D A054200 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 A054200 N. J. A. Sloane, <a href="http://neilsloane.com/doc/dijen.txt">On single-deletion-correcting codes</a>
%H A054200 N. J. A. Sloane, <a href="http://neilsloane.com/doc/dijen.pdf">On single-deletion-correcting codes</a>, 2002.
%e A054200 From _Seiichi Manyama_, Sep 02 2023: (Start)
%e A054200 1 + 2 == 3 mod 6,
%e A054200 3 == 3 mod 6,
%e A054200 1 + 3 + 5 == 3 mod 6,
%e A054200 2 + 3 + 4 == 3 mod 6,
%e A054200 4 + 5 == 3 mod 6,
%e A054200 1 + 2 + 3 + 4 + 5 == 3 mod 6.
%e A054200 So a(5) = 6. (End)
%o A054200 (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 A054200 For the codes VT_0(n), VT_1(n), VT_2(n) see resp. A000016, A000048, A000048 (again).
%Y A054200 Cf. A000010, A008683, A053633.
%K A054200 nonn
%O A054200 0,3
%A A054200 _N. J. A. Sloane_, Apr 29 2000
%E A054200 Offset changed to 0 by _Seiichi Manyama_, Sep 02 2023