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.

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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.

Cf. A023531. A023532.

Sequence in context: A058062 A102820 A355717 * A024880 A029424 A061498

Adjacent sequences: A024314 A024315 A024316 * A024318 A024319 A024320

Keyword

nonn

Author

Clark Kimberling

Status

approved