A357355 Number of nonempty subsets of {1..n} whose elements have an odd average.

1, 1, 2, 4, 9, 13, 20, 38, 71, 119, 206, 384, 713, 1285, 2356, 4428, 8331, 15569, 29270, 55582, 105717, 200847, 382808, 732744, 1404667, 2694391, 5178186, 9973416, 19233457, 37125547, 71754692, 138871244, 269038123, 521666967, 1012485750, 1966957674, 3824314685

Offset

1,3

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = A051293(n) - A357356(n). - Michael S. Branicky, Sep 25 2022

Example

a(6) = 13 subsets: {1}, {3}, {5}, {1, 5}, {2, 4}, {4, 6}, {1, 2, 6}, {1, 3, 5}, {2, 3, 4}, {4, 5, 6}, {1, 2, 3, 6}, {1, 2, 4, 5} and {1, 2, 3, 4, 5}.

Prog

(Python)
from functools import lru_cache
def cond(s, c): q, r = divmod(s, c); return r == 0 and q&1
@lru_cache(maxsize=None)
def b(n, s, c):
    if n == 0: return int (c > 0 and cond(s, c))
    return b(n-1, s, c) + b(n-1, s+n, c+1)
a = lambda n: b(n, 0, 0)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Sep 25 2022

Crossrefs

Cf. A051293, A309160, A357356.

Sequence in context: A024925 A162342 A162761 * A114885 A049793 A090942

Adjacent sequences: A357352 A357353 A357354 * A357356 A357357 A357358

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 25 2022

Extensions

a(24)-a(37) from Michael S. Branicky, Sep 25 2022

Status

approved