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

Author

Ilya Gutkovskiy, Dec 09 2020

Keywords

• nonn

Examples

			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}.
		

Links

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

Crossrefs

Cf. A000290, A126024, A336815.

Programs

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

Formula

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

Extensions

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