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

0,3

Links

Table of n, a(n) for n=0..65.

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".

Formula

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

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 *)

Crossrefs

Essentially the same as A047273.

Sequence in context: A154611 A189669 A164028 * A047273 A342051 A232744

Adjacent sequences: A301726 A301727 A301728 * A301730 A301731 A301732

Keyword

nonn

Author

N. J. A. Sloane, Mar 30 2018

Status

approved