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A304371
Number of function calls of the second kind required to compute ack(3,n), where ack denotes the Ackermann function.
3
5, 47, 257, 1187, 5093, 21095, 85865, 346475, 1391981, 5580143, 22345073, 89429363, 357815669, 1431459191, 5726229881, 22905705851, 91624396157, 366500730239, 1466009212289, 5864049431939, 23456222893445, 93824941905287, 375299868284297, 1501199674463627
OFFSET
0,1
COMMENTS
The distinction between different kinds of recursive calls is based on a naive implementation of the Ackermann function in C.
int ack(int m, int n)
{
// Final result
....if (m==0) return n + 1;
.
// Recursive calls of the first kind:
....if (n==0) return ack(m - 1, 1);
.
// Recursive calls of the second kind:
....return ack(m - 1, ack(m, n - 1));
}
FORMULA
A304370(n) + a(n) + 1 = A074877(n).
G.f.: (8*x^3-14*x^2+7*x+5)/((4*x-1)*(2*x-1)*(x-1)^2). - Alois P. Heinz, May 12 2018
MATHEMATICA
LinearRecurrence[{8, -21, 22, -8}, {5, 47, 257, 1187}, 30] (* Harvey P. Dale, Oct 22 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, May 11 2018
STATUS
approved