A339612 Number of sets of distinct positive integers whose sum of squares is a square, the largest integer of a set is n.

1, 1, 1, 2, 1, 3, 2, 5, 9, 11, 32, 51, 113, 184, 364, 605, 1175, 2077, 3749, 7108, 12214, 23871, 42474, 82212, 153738, 288842, 555593, 1041563, 2016299, 3809565, 7302893, 13914139, 26591478, 50942383, 97411030, 186943685, 358286670, 689827822, 1326042612, 2558758426

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Formula

a(n) = A336815(n) - A336815(n-1).

Example

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

Prog

(Python)
a = lambda n: b(n-1, n*n, 1) # for b() in A336815
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Dec 10 2020

Crossrefs

Cf. A000290, A126024, A336815.

Sequence in context: A176741 A266138 A014000 * A075257 A260618 A306286

Adjacent sequences: A339609 A339610 A339611 * A339613 A339614 A339615

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 09 2020

Extensions

a(24)-a(40) from Michael S. Branicky, Dec 09 2020

Status

approved