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A339484 Number of subsets of {1..n} whose cardinality is equal to the average of the elements. 2
1, 1, 2, 3, 4, 7, 11, 17, 28, 47, 80, 139, 245, 436, 784, 1419, 2585, 4738, 8729, 16154, 30015, 55966, 104682, 196378, 369384, 696494, 1316252, 2492683, 4729673, 8990374, 17118020, 32644544, 62345875, 119235519, 228333179, 437790086, 840362539, 1614894770, 3106516468 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..300

Eric W. Weisstein's World of Mathematics, Arithmetic Mean

EXAMPLE

a(6) = 7 subsets: {1}, {1, 3}, {1, 2, 6}, {1, 3, 5}, {2, 3, 4}, {1, 4, 5, 6} and {2, 3, 5, 6}.

PROG

(Python)

from itertools import combinations

def a(n):

    ss, s = 0, range(1, n+1)

    for r in range(1, n+1):

        rr = r*r

        ss += sum(sum(subs)==rr for subs in combinations(s, r))

    return ss

print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Dec 06 2020

(Python)

from functools import lru_cache

from itertools import combinations

@lru_cache(maxsize=None)

def A339484(n):

    return 1 if n == 1 else A339484(n-1)+sum(sum(d)+n==(i+1)**2 for i in range(1, n) for d in combinations(range(1, n), i)) # Chai Wah Wu, Dec 07 2020

CROSSREFS

Cf. A051293, A126024.

Sequence in context: A303025 A346020 A192669 * A072164 A060987 A006259

Adjacent sequences:  A339481 A339482 A339483 * A339485 A339486 A339487

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 06 2020

EXTENSIONS

a(24)-a(32) from Michael S. Branicky, Dec 06 2020

a(33)-a(35) from Chai Wah Wu, Dec 07 2020

a(36)-a(39) from Michael S. Branicky, Dec 08 2020

STATUS

approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)