A024324 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 = A000201 (lower Wythoff sequence).

0, 0, 3, 4, 6, 8, 9, 11, 20, 23, 27, 29, 33, 37, 39, 43, 60, 65, 70, 74, 80, 84, 89, 94, 98, 104, 131, 137, 143, 150, 157, 163, 169, 176, 183, 189, 195, 202, 241, 248, 256, 265, 272, 281, 289, 296, 306, 313, 321, 329, 337, 346, 397, 406, 416, 425, 436, 445, 454, 466, 474, 484

Offset

1,3

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)*A000201(n-j+1).

Mathematica

Table[t=0; m=3; p=BitShiftRight[n]; n--; While[n>p, t += Floor[n*GoldenRatio^2]; n -= m++]; t, {n, 120}] (* G. C. Greubel, Jan 28 2022 *)

Prog

(Magma)
b:= func< n, j | IsIntegral((Sqrt(8*j+9) -3)/2) select Fibonacci(n-j+1) else 0 >;
A024324:= func< n | (&+[b(n, j): j in [1..Floor((n+1)/2)]]) >;
[A024324(n) : n in [1..80]]; // G. C. Greubel, Jan 28 2022
(Sage)
def b(n, j): return floor( (n+1-j)*(1+sqrt(5))/2 ) if ((sqrt(8*j+9) -3)/2).is_integer() else 0
def A024324(n): return sum( b(n, k) for k in (1..((n+1)//2)) )
[A024324(n) for n in (1..80)] # G. C. Greubel, Jan 28 2022
(PARI) my(phi=quadgen(5)); a(n) = my(L=n>>1, m=2, ret=0); n--; while(n>L, ret += floor(n*phi); n-=(m++)); ret; \\ Kevin Ryde, Feb 03 2022

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024325, A024326, A024327.

Cf. A000201, A023531.

Sequence in context: A138924 A188015 A192284 * A255773 A195019 A288601

Adjacent sequences: A024321 A024322 A024323 * A024325 A024326 A024327

Keyword

nonn

Author

Clark Kimberling

Extensions

a(62) corrected by Sean A. Irvine, Jun 27 2019

Status

approved