A350287 Number of solutions to +-1 +- 3 +- 6 +- 10 +- ... +- n*(n + 1)/2 = 0 or 1.

1, 1, 0, 0, 2, 1, 2, 2, 4, 7, 12, 16, 26, 42, 66, 104, 210, 318, 620, 970, 1748, 3281, 5948, 10480, 18976, 34233, 60836, 111430, 209460, 378529, 704934, 1284836, 2387758, 4466874, 8331820, 15525814, 28987902, 54162165, 101242982, 190267598, 358969426, 674845081

Offset: 0

Author

Ilya Gutkovskiy, Jan 19 2022

Keywords

• nonn

Examples

			a(4) = 2: -1 - 3 - 6 + 10 = +1 + 3 + 6 - 10 = 0.
		

Crossrefs

Cf. A000217, A025591, A058498, A158380.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def b(n, i):
    if n > i*(i+1)*(i+2)//6: return 0
    if i == 0: return 1
    return b(n+i*(i+1)//2, i-1) + b(abs(n-i*(i+1)//2), i-1)
def a(n): return b(0, n) + b(1, n)
print([a(n) for n in range(41)]) # Michael S. Branicky, Jan 19 2022