A301729 a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.

1, 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 63, 65, 66, 67, 69, 71, 72, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 96, 97

Offset: 0

Author

N. J. A. Sloane, Mar 30 2018

Keywords

• nonn

Links

• A. V. Shutov, The number of words of a given length in the planar crystallographic groups, (in Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Vol. 302 (2003), Anal. Teor. Chisel i Teor. Funkts. 19, pp. 188-197, 203; translation, in J. Math. Sci. (N.Y.), Vol. 129, No. 3 (2005), pp. 3922-3926 [MR2023041]. See Table 1, line "p31m".

Crossrefs

Essentially the same as A047273.

Programs

Maple

f:= proc(n) if n=0 then 1
elif (n mod 4) = 0 then (3*n)/2
elif (n mod 4) = 1 then (3*n-1)/2
elif (n mod 4) = 2 then (3*n)/2
else (3*n+1)/2 fi;
end;
s1 := [seq(f(n),n=0..70)];

Mathematica

Join[{1}, Select[Range[100], MemberQ[{0, 1, 3, 5}, Mod[#,6]] &]] (* Amiram Eldar, Dec 31 2021 *)

Formula

Sum_{n>=1} (-1)^(n+1)/a(n) = log(108)/6 = log(2)/3 + log(3)/2. - Amiram Eldar, Dec 31 2021