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A339569 Number of subsets of {1..n} whose cardinality is equal to the root-mean-square of the elements. 0
1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 5, 10, 16, 32, 56, 90, 134, 186, 304, 476, 746, 1308, 2522, 4845, 9129, 17260, 32684, 59908, 106181, 191779, 337793, 596689, 1061991, 1907311, 3518903, 6426672, 12093858, 22777645, 42886411, 81002076, 151575988, 285280108, 529313088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..43.

Eric Weisstein's World of Mathematics, Root-Mean-Square

EXAMPLE

a(12) = 10 subsets: {1}, {1, 2, 4, 5, 7, 11}, {1, 3, 5, 6, 8, 9}, {3, 4, 5, 6, 7, 9}, {1, 2, 3, 6, 7, 10, 12}, {2, 3, 4, 5, 8, 9, 12}, {2, 3, 6, 7, 8, 9, 10}, {3, 4, 5, 6, 7, 8, 12}, {1, 2, 5, 6, 9, 10, 11, 12} and {1, 4, 6, 7, 8, 9, 11, 12}.

PROG

(Python)

from functools import lru_cache

@lru_cache(maxsize=None)

def b(n, sos, c):

  if n == 0:

    if c>0:

      if sos==c*c*c: return 1

    return 0

  return b(n-1, sos, c) + b(n-1, sos+n*n, c+1)

a = lambda n: b(n, 0, 0)

print([a(n) for n in range(1, 44)]) # Michael S. Branicky, Dec 10 2020

CROSSREFS

Cf. A092670, A339454, A339484.

Sequence in context: A176848 A058615 A082612 * A170926 A122413 A297661

Adjacent sequences:  A339566 A339567 A339568 * A339570 A339571 A339572

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 09 2020

EXTENSIONS

a(24)-a(43) from Michael S. Branicky, Dec 09 2020

STATUS

approved

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Last modified October 27 23:46 EDT 2021. Contains 348305 sequences. (Running on oeis4.)