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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).
20
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
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
KEYWORD
nonn
STATUS
approved