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A024317
a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A023532.
17
0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 4, 4, 3, 4, 3, 4, 3, 3, 4, 4, 3, 4, 5, 5, 4, 5, 4, 4, 5, 3, 5, 5, 5, 4, 5, 5, 5, 6, 5, 5, 6, 6, 5, 5, 5, 6, 6, 5, 5, 6, 5, 6, 7, 7, 5, 7, 7, 7, 7, 4, 7, 6, 6, 7, 7, 6, 6, 7, 7, 7, 8, 7
OFFSET
1,11
LINKS
FORMULA
a(n) = Sum_{k=1..floor((n+1)/2)} A023531(k)*A023532(n-k+1). - G. C. Greubel, Jan 19 2022
MATHEMATICA
A023531[n_]:= SquaresR[1, 8n+9]/2;
a[n_]:= Sum[A023531[j]*(1 - A023531[n-j+1]), {j, Floor[(n+1)/2]}];
Table[a[n], {n, 90}] (* G. C. Greubel, Jan 19 2022 *)
PROG
(Magma)
A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*(1 - A023531(n-j+1)): j in [1..Floor((n+1)/2)]]) : n in [1..90]]; // G. C. Greubel, Jan 19 2022
(Sage)
def A023531(n):
if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
else: return 0
[sum( A023531(j)*(1-A023531(n-j+1)) for j in (1..floor((n+1)/2)) ) for n in (1..90)] # G. C. Greubel, Jan 19 2022
KEYWORD
nonn
STATUS
approved