A024322 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 = (F(2), F(3), ...).

0, 0, 2, 3, 5, 8, 13, 21, 42, 68, 110, 178, 288, 466, 754, 1220, 2029, 3283, 5312, 8595, 13907, 22502, 36409, 58911, 95320, 154231, 250161, 404769, 654930, 1059699, 1714629, 2774328, 4488957, 7263285

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, A024323, A024324, A024325, A024326, A024327.

Cf. A000045, A010054, A023531.

Programs

Magma

A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*Fibonacci(n-j+2): j in [1..Floor((n+1)/2)]]) : n in [1..40]]; // G. C. Greubel, Jan 20 2022

Mathematica

A010054[n_]:= SquaresR[1, 8n+1]/2;
a[n_]:= Sum[A010054[j+1]*Fibonacci[n-j+2], {j, Floor[(n+1)/2]}];
Table[a[n], {n, 40}] (* 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)*fibonacci(n-j+2) for j in (1..floor((n+1)/2)) ) for n in (1..40)] # G. C. Greubel, Jan 20 2022

Formula

From G. C. Greubel, Jan 20 2022: (Start)

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A000045(n-j+1).

a(n) = Sum_{j=1..floor((n+1)/2)} A010054(j+1)*A000045(n-j+2). (End)