A087917 Number of unordered ways to write n as a sum of 3 odious numbers (A000069).

0, 0, 1, 1, 1, 2, 1, 1, 2, 3, 2, 3, 3, 2, 4, 6, 5, 5, 6, 5, 6, 8, 8, 9, 9, 8, 10, 12, 12, 14, 14, 10, 14, 19, 14, 18, 20, 14, 19, 25, 21, 20, 27, 22, 23, 32, 26, 27, 31, 29, 31, 36, 35, 35, 39, 34, 38, 47, 40, 42, 47, 40, 43, 60, 53, 44, 60, 50, 48, 68, 62, 54, 64, 65, 58, 75

Offset

1,6

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 200 terms from Robert Price)

Formula

a(n) = Sum_{i+j+k = n} A010060(i)*A010060(j)*A010060(k). - Benoit Cloitre, Mar 19 2004

Example

a(6) = 2 as 6 = 1 + 1 + 4 = 2 + 2 + 2. 1, 2 and 4 are odious as the number of ones in the binary expansion is odd. The partition 1 + 2 + 3 does not count as 3 is not odious; the number of ones in the binary expansion of 3 is 2 (even). - David A. Corneth, Apr 23 2025

Mathematica

A010060 = Cases[Import["https://oeis.org/A010060/b010060.txt", "Table"], {_, _}][[All, 2]];
Table[Length@Select[DeleteDuplicates[Sort /@ Select[Tuples[Range[n], 3], Total[#] == n &]], A010060[[#[[1]] + 1]]*A010060[[#[[2]] + 1]]* A010060[[#[[3]] + 1]] == 1 &], {n, 200}] (* Robert Price, Apr 22 2025 *)

Prog

(PARI) a(n)=sum(i=1, n, sum(j=1, i, sum(k=1, j, if(i+j+k-n, 0, A010060(i)*A010060(j)*A010060(k)))))
(PARI) first(n) = {
    res = vector(n);
    for(i = 1, n\3,
        if(bitand(hammingweight(i), 1),
            for(j = i, (n - i)\2,
                if(bitand(hammingweight(j), 1),
                    for(k = j, n - i - j,
                        res[i+j+k]+=bitand(hammingweight(k), 1)))))); res
} \\ David A. Corneth, Apr 23 2025

Crossrefs

Cf. A000069, A087916.

Cf. A010060.

Sequence in context: A091093 A049615 A114919 * A330334 A087741 A054991

Adjacent sequences: A087914 A087915 A087916 * A087918 A087919 A087920

Keyword

nonn,easy

Author

Ralf Stephan, Oct 18 2003

Status

approved