OFFSET
0,3
COMMENTS
Comment from Franklin T. Adams-Watters, Jul 13 2006: This is the number of subpartitions of the sequence 3^n-1. As such it can also be computed adding forward, with 3^n terms in the n-th line:
1...........................................................................
1.1 1.......................................................................
1.2.3.3..3..3..3..3..3......................................................
1.3.6.9.12.15.18.21.24.24.24.24.24.24.24.24.24.24.24.24.24.24.24.24.24.24.24
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..65
EXAMPLE
For example, for n=3 the array looks like this:
1..1..1..1..1........1..1..1..1..1..1..1..1..1..1
........................1..2..3..4..5..6..7..8..9
..........................................7.15.24
...............................................24
Therefore a(3)=24.
MAPLE
proc(n::nonnegint) local f, a; if n=0 or n=1 then return 1; end if; f:=L->[seq(add(L[i], i=2*nops(L)/3+1..j), j=2*nops(L)/3+1..nops(L))]; a:=f([seq(1, j=1..3^n)]); while nops(a)>3 do a:=f(a) end do; a[3]; end proc;
MATHEMATICA
A[n_, k_] := A[n, k] = If[n == 0, 1, -Sum[A[j, k]*(-1)^(n - j)*Binomial[If[j == 0, 1, k^j], n - j], {j, 0, n - 1}]];
a[n_] := A[n, 3];
CROSSREFS
KEYWORD
nonn
AUTHOR
Augustine O. Munagi, Jun 17 2005
EXTENSIONS
More terms from Paul D. Hanna
STATUS
approved