OFFSET
1,5
COMMENTS
a(n) is the coefficient of x^(n*(n+3)/4-1) of Product_{k=2..n} (1+x^k)). - Jianing Song, Nov 19 2021
LINKS
Jianing Song, Table of n, a(n) for n = 1..1000
PROG
(C)
int solsN(int n, int k, int sum) { if (n == k) return sum == n; return solsN(n, k+1, sum + k + 1) + solsN(n, k+1, sum - k - 1); }
int getNumber(int n) { return solsN(n, 1, 1); }
(Python)
from functools import cache
@cache
def b(t, s, u): # target, sum, upto
if u == 1: return int(t == s + 1)
return b(t, s - u, u - 1) + b(t, s + u, u - 1)
def a(n): return b(n, 0, n)
print([a(n) for n in range(1, 49)]) # Michael S. Branicky, Oct 29 2021
(PARI) list(n) = my(poly=vector(n), v=vector(n)); poly[1]=1; for(k=2, n, poly[k]=poly[k-1]*(1+'x^k)); for(k=1, n, if(k%4==2||k%4==3, v[k]=0, v[k]=polcoeff(poly[k], k*(k+3)/4-1))); v \\ Jianing Song, Nov 19 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Cortild, Oct 26 2021
EXTENSIONS
a(30)-a(48) from Michael S. Branicky, Oct 29 2021
STATUS
approved