A024318 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 = (Fibonacci numbers).

0, 0, 1, 2, 3, 5, 8, 13, 26, 42, 68, 110, 178, 288, 466, 754, 1254, 2029, 3283, 5312, 8595, 13907, 22502, 36409, 58911, 95320, 154608, 250161, 404769, 654930, 1059699, 1714629, 2774328, 4488957, 7263285

Offset

1,4

Links

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

Formula

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*Fibonacci(n-j+1). - G. C. Greubel, Jan 19 2022

Mathematica

Table[t=0; m=3; p=BitShiftRight[n]; n--; While[n>p, t += Fibonacci[n+1]; n -= m++]; t, {n, 120}] (* G. C. Greubel, Jan 19 2022 *)

Prog

(Magma)
b:= func< n, j | IsIntegral((Sqrt(8*j+9) -3)/2) select Fibonacci(n-j+1) else 0 >;
A024318:= func< n | (&+[b(n, j): j in [1..Floor((n+1)/2)]]) >;
[A024318(n) : n in [1..80]]; // G. C. Greubel, Jan 19 2022
(Sage)
def b(n, j): return fibonacci(n-j+1) if ((sqrt(8*j+9) -3)/2).is_integer() else 0
def A024318(n): return sum( b(n, j) for j in (1..floor((n+1)/2)) )
[A024318(n) for n in (1..120)] # G. C. Greubel, Jan 19 2022

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.

Cf. A000045, A023531.

Sequence in context: A340708 A074030 A336604 * A324738 A132915 A030036

Adjacent sequences: A024315 A024316 A024317 * A024319 A024320 A024321

Keyword

nonn

Author

Clark Kimberling

Status

approved