A177888 P_n(k) with P_0(z) = z+1 and P_n(z) = z + P_(n-1)(z)*(P_(n-1)(z)-z) for n>1; square array P_n(k), n>=0, k>=0, read by antidiagonals.
1, 2, 1, 3, 3, 1, 4, 5, 7, 1, 5, 7, 17, 43, 1, 6, 9, 31, 257, 1807, 1, 7, 11, 49, 871, 65537, 3263443, 1, 8, 13, 71, 2209, 756031, 4294967297, 10650056950807, 1, 9, 15, 97, 4691, 4870849, 571580604871, 18446744073709551617, 113423713055421844361000443, 1
Offset: 0
Examples
Square array P_n(k) begins: 1, 2, 3, 4, 5, 6, 7, 8, ... 1, 3, 5, 7, 9, 11, 13, 15, ... 1, 7, 17, 31, 49, 71, 97, 127, ... 1, 43, 257, 871, 2209, 4691, 8833, 15247, ... 1, 1807, 65537, 756031, 4870849, ... 1, 3263443, 4294967297, ... 1, 10650056950807, ...
Links
- Alois P. Heinz, Antidiagonals n = 0..13, flattened
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
Crossrefs
Programs
-
Maple
p:= proc(n) option remember; z-> z+ `if`(n=0, 1, p(n-1)(z)*(p(n-1)(z)-z)) end: seq(seq(p(n)(d-n), n=0..d), d=0..8); -
Mathematica
p[n_] := p[n] = Function[z, z + If [n == 0, 1, p[n-1][z]*(p[n-1][z]-z)] ]; Table [Table[p[n][d-n], {n, 0, d}], {d, 0, 8}] // Flatten (* Jean-François Alcover, Dec 13 2013, translated from Maple *)