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

0,7

Links

Table of n, a(n) for n=0..45.

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A181839 A100939 A099925 * A201563 A016644 A240966

Adjacent sequences: A350999 A351000 A351001 * A351003 A351004 A351005

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2022

Status

approved