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A074877
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Number of function calls required to compute ack(3,n), where ack denotes the Ackermann function.
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0
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15, 106, 541, 2432, 10307, 42438, 172233, 693964, 2785999, 11164370, 44698325, 178875096, 715664091, 2862983902, 11452590817, 45811673828, 183249316583, 733002509034, 2932020521709, 11728103058160, 46912454175475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The Ackermann function is defined recursively for nonnegative integers m,n by: ack(0,n) = n + 1 if m=0; ack(m,0) = ack(m-1,1) if m>0 and n=0; ack(m,n) = ack(m-1,ack(m,n-1)) otherwise.
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REFERENCES
| Y. Sundblad, The Ackermann function. A theoretical, computational and formula manipulative study. Nordisk Tidskr. Informationsbehandling (BIT) 11 1971 107-119.
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LINKS
| Gert Bultman, Ackermann function.
E. Weisstein, Ackermann function.
Wikipedia, Ackermann function.
Index to sequences with linear recurrences with constant coefficients, signature (8,-21,22,-8).
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FORMULA
| G.f.: (15-14*x+8*x^2)/((4*x-1)*(2*x-1)*(x-1)^2); recurrence: a(n) = 8*a(n-1)-21*a(n-2)+22*a(n-3)-8*a(n-4); a(n) = 128/3*4^n-40*2^n+3*n+37/3 for n>=0 - Pab Ter (pabrlos(AT)yahoo.com), May 29 2004
a(n) ~ 128/3*4^n. [Charles R Greathouse IV, Dec 09 2011]
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PROG
| (PARI) a(n)=128/3*4^n-40*2^n+3*n+37/3 \\ Charles R Greathouse IV, Dec 09 2011
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CROSSREFS
| Sequence in context: A012507 A143727 A041426 * A202255 A205352 A055504
Adjacent sequences: A074874 A074875 A074876 * A074878 A074879 A074880
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KEYWORD
| nonn,easy
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AUTHOR
| Jeff Medha (medha_jeff(AT)yahoo.co.in), Sep 12 2002
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EXTENSIONS
| Edited by Pab Ter (pabrlos(AT)yahoo.com), May 29 2004
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