A351002 Number of solutions to +-1 +- 3 +- 6 +- 10 +- ... +- n*(n + 1)/2 = n.
1, 1, 1, 0, 0, 1, 3, 0, 4, 3, 9, 0, 27, 43, 71, 0, 190, 318, 604, 0, 1846, 3127, 5664, 0, 19048, 34065, 62045, 0, 205713, 378243, 705836, 0, 2403370, 4434940, 8276125, 0, 28980680, 54167797, 101541048, 0, 358095372, 674776903, 1274888645, 0, 4551828850, 8612421500
Offset: 0
Keywords
Programs
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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(n, n) print([a(n) for n in range(50)]) # Michael S. Branicky, Jan 29 2022
Formula
a(n) = [x^n] Product_{k=1..n} (x^(k*(k+1)/2) + 1/x^(k*(k+1)/2)).