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.

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

Author

Clark Kimberling

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.

Cf. A023531.

Programs

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

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 *)

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

Formula

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A023531(n-j+1). - G. C. Greubel, Jan 17 2022