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A143077
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This is the n-th term of a pseudo-Fibonacci sequence created by applying the function fib(1,...,n) to itself n times.
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1
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1, 1, 4, 31, 485, 27343, 3595117, 1359551201, 1310562076858, 3378072688461451, 22702751567715567129, 401359405793550977993221, 18572242457139030215454649193, 2252593125544789695036793639095505
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence grows faster than any exponential sequence. The implementation here is quite slow.
Let g(x) be fib(1,1,x), g returns y; let h(y) be fib(1,y,x), h returns z; let i(z) be z be applied to itself x-1 times. Then f(x) = i(h(g(x)))
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EXAMPLE
| E.g. n=1 fib(1,1,n) n=2 fib(1,fib(1,1,n),n) n=3 fib(1,fib(1,fib(1,1,n),n),n) ...
f(3) is fib(1,fib(1,fib(1,1,3),3),3)
f(3) simplifies to fib(1,fib(1,2,3),3)
f(3) simplifies to fib(1,3,3)
f(3) is 4
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PROG
| .Python program (replace leading dots by spaces):
.#This is Python, use slowfibnd(x) to generate the xth term.
.from string import *
.def fib(arb1, arb2, nth):
.....if n-th == 0:
.........return arb1
.....if n-th == 1:
.........return arb2
.....x = [0]*nth
.....x[0] = arb1
.....x[1] = arb2
.....for i in xrange(2, nth, 1):
.........x[i] = x[i-1]+x[i-2]
.....return x[-1]
.def fib2d(n):
.....return fib(1, fib(1, 1, n), n)
.def fib3d(n):
.....return fib(1, fib(1, fib(1, 1, n), n), n)
.def slowfibnd(n): #This is an inelegant solution, but it will work
.....begin = "fib(1, 0+1, n)"
.....for x in range(n-1):
.........begin = replace(begin, '0+1', 'fib(1, 0+1, n)')
.....return eval(begin)
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CROSSREFS
| Cf. A000045 is the Fibonacci function fib(1, 1, n), A142975 is the Fibonacci function applied to itself fib(1, fib(1, 1, n), n).
Sequence in context: A174324 A195195 A141827 * A203011 A005841 A005828
Adjacent sequences: A143074 A143075 A143076 * A143078 A143079 A143080
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KEYWORD
| nonn
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AUTHOR
| Gregory Nisbet (gregory.nisbet(AT)gmail.com), Jul 22 2008
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