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A074877 Number of function calls required to compute ack(3,n), where ack denotes the Ackermann function. 5
15, 106, 541, 2432, 10307, 42438, 172233, 693964, 2785999, 11164370, 44698325, 178875096, 715664091, 2862983902, 11452590817, 45811673828, 183249316583, 733002509034, 2932020521709, 11728103058160, 46912454175475, 187649900587766, 750599770123001, 3002399416036092 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..23.

Gert Bultman, Ackermann function.

Y. Sundblad, The Ackermann function. A theoretical, computational and formula manipulative study, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 107-119.

E. Weisstein, Ackermann function.

Wikipedia, Ackermann function.

Index entries for linear recurrences with constant coefficients, signature (8,-21,22,-8).

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]

MATHEMATICA

Table[128 / 3 4^n - 40 2^n + 3 n + 37 / 3, {n, 0, 30}] (* Vincenzo Librandi, Apr 19 2015 *)

PROG

(PARI) a(n)=128/3*4^n-40*2^n+3*n+37/3 \\ Charles R Greathouse IV, Dec 09 2011

(MAGMA) [128/3*4^n-40*2^n+3*n+37/3: n in [0..30]]; // Vincenzo Librandi, Apr 19 2015

CROSSREFS

Sequence in context: A041426 A278781 A275644 * A293263 A202255 A243212

Adjacent sequences:  A074874 A074875 A074876 * A074878 A074879 A074880

KEYWORD

nonn,easy

AUTHOR

Jeff Medha (medha_jeff(AT)yahoo.co.in), Sep 12 2002

EXTENSIONS

Edited by Pab Ter (pabrlos(AT)yahoo.com), May 29 2004

More terms from Vincenzo Librandi, Apr 19 2015

STATUS

approved

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Last modified March 19 00:03 EDT 2019. Contains 321305 sequences. (Running on oeis4.)