OFFSET
0,3
LINKS
Gandhar Joshi, Table of n, a(n) for n = 0..1000
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) + 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
KEYWORD
base,nonn
AUTHOR
Gandhar Joshi, May 16 2023
STATUS
approved