A024323 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 = (odd natural numbers).

0, 0, 3, 5, 7, 9, 11, 13, 24, 28, 32, 36, 40, 44, 48, 52, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 295, 305, 315, 325, 335, 345, 355, 365, 375, 385, 395, 405, 415, 425, 488, 500, 512, 524, 536, 548, 560, 572, 584

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024324, A024325, A024326, A024327.

Cf. A023531.

Programs

Magma

A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*(2*n-2*j+1): j in [1..Floor((n+1)/2)]]) : n in [1..70]]; // G. C. Greubel, Jan 20 2022

Mathematica

A023531[n_]:= SquaresR[1, 8n+9]/2;
a[n_]:= Sum[A023531[j]*(2*n-2*j+1), {j, Floor[(n+1)/2]}];
Table[a[n], {n, 70}] (* G. C. Greubel, Jan 20 2022 *)

Sage

def A023531(n):
    if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
    else: return 0
[sum( A023531(j)*(2*n-2*j+1) for j in (1..floor((n+1)/2)) ) for n in (1..70)] # G. C. Greubel, Jan 20 2022

Formula

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*(2*n -2*j + 1). - G. C. Greubel, Jan 20 2022