A339569 Number of subsets of {1..n} whose cardinality is equal to the root-mean-square of the elements.

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

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