A351002 - OEIS

%I #13 Feb 04 2022 11:20:30

%S 1,1,1,0,0,1,3,0,4,3,9,0,27,43,71,0,190,318,604,0,1846,3127,5664,0,

%T 19048,34065,62045,0,205713,378243,705836,0,2403370,4434940,8276125,0,

%U 28980680,54167797,101541048,0,358095372,674776903,1274888645,0,4551828850,8612421500

%N Number of solutions to +-1 +- 3 +- 6 +- 10 +- ... +- n*(n + 1)/2 = n.

%F a(n) = [x^n] Product_{k=1..n} (x^(k*(k+1)/2) + 1/x^(k*(k+1)/2)).

%o (Python)

%o from functools import lru_cache

%o @lru_cache(maxsize=None)

%o def b(n, i):

%o     if n > i*(i+1)*(i+2)//6: return 0

%o     if i == 0: return 1

%o     return b(n+i*(i+1)//2, i-1) + b(abs(n-i*(i+1)//2), i-1)

%o def a(n): return b(n, n)

%o print([a(n) for n in range(50)]) # _Michael S. Branicky_, Jan 29 2022

%Y Cf. A000217, A058498, A063890, A158380, A348165, A350287.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jan 29 2022