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A363070
Take the terms 0..n of the infinite Fibonacci word A003849, regard them as a number in Fibonacci base.
1
0, 1, 2, 3, 6, 10, 17, 28, 45, 74, 120, 194, 315, 510, 826, 1337, 2163, 3501, 5665, 9167, 14833, 24000, 38834, 62835, 101669, 164505, 266175, 430681, 696857, 1127538, 1824396, 2951935, 4776331, 7728267, 12504599, 20232867, 32737467, 52970334, 85707802, 138678137, 224385940, 363064078
OFFSET
0,3
LINKS
Agnibha Banerjee, Python Program, May 16 2023.
FORMULA
a(n) = Sum_{i=0..n} A003849(i)*Fibonacci(n-i+2).
a(n) = a(n-1) + a(n-2) + A003849(n) + A003849(n-1).
a(n) = a(n-1) + a(n-2) + A005713(n-1). - Kevin Ryde, May 20 2023
EXAMPLE
0 -> 0 -> a(0) = 0,
0,1 -> 01 -> a(1) = 1,
0,1,0 -> 010 -> a(2) = 2,
0,1,0,0 -> 0100 -> a(3) = 3,
0,1,0,0,1 -> 01001 -> a(4) = 6,
0,1,0,0,1,0 -> 010010 -> a(5) = 10,
0,1,0,0,1,0,1 -> 0100101 -> a(6) = 17,
0,1,0,0,1,0,1,0 -> 01001010 -> a(7) = 28,
0,1,0,0,1,0,1,0,0 -> 010010100 -> a(8) = 45,
0,1,0,0,1,0,1,0,0,1 -> 0100101001 -> a(9) = 74.
PROG
(Python) # see linked program
(Python)
def aupto(n): # produces n terms, indices 0..n-1
F1, F, a = [0], [0, 1], [0, 1]
while len(F) < n:
F1, F = F, F+F1
[a.append(a[-2]+a[-1]+F[i]+F[i-1]) for i in range(2, n)]
return a
print(aupto(42)) # Michael S. Branicky, May 17 2023
CROSSREFS
Cf. A003849 (Fibonacci word), A005713, A189920 (Zeckendorf digits).
Cf. A182028.
Sequence in context: A099517 A026647 A026669 * A023614 A001610 A324015
KEYWORD
base,nonn
AUTHOR
Gandhar Joshi, May 16 2023
STATUS
approved