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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).
17
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
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
KEYWORD
nonn
EXTENSIONS
a(62) corrected by Sean A. Irvine, Jun 27 2019
STATUS
approved