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A024316
a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = A023531.
19
0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1
OFFSET
1,28
LINKS
FORMULA
a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A023531(n-j+1). - G. C. Greubel, Jan 17 2022
MATHEMATICA
A023531[n_]:= SquaresR[1, 8n+9]/2;
a[n_]:= a[n]= Sum[A023531[j]*A023531[n-j+1], {j, Floor[(n+1)/2]}];
Table[a[n], {n, 110}] (* G. C. Greubel, Jan 17 2022 *)
PROG
(Haskell)
a024316 n = sum $ take (div (n + 1) 2) $ zipWith (*) zs $ reverse zs
where zs = take n $ tail a023531_list
-- Reinhard Zumkeller, Feb 14 2015
(Magma)
A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*A023531(n-j+1): j in [1..Floor((n+1)/2)]]) : n in [1..110]]; // G. C. Greubel, Jan 17 2022
(Sage)
def A023531(n):
if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
else: return 0
[sum( A023531(j)*A023531(n-j+1) for j in (1..floor((n+1)/2)) ) for n in (1..110)] # G. C. Greubel, Jan 17 2022
KEYWORD
nonn
STATUS
approved