OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..5000
EXAMPLE
a(10) = #{8+2, 7+1+1+1, 6+3+1, 6+2+2, 6+2+1+1, 5+5, 5+4+1, 5+1+1+1+1+1, 4+4+2, 4+3+3, 4+3+1+1+1, 4+2+2+2, 4+2+2+1+1, 4+2+1+1+1+1, 3+3+3+1, 3+3+1+1+1+1, 3+1+1+1+1+1+1+1, 2+2+2+2+2, 2+2+2+2+1+1, 2+2+2+1+1+1+1, 2+2+1+1+1+1+1+1, 2+1+1+1+1+1+1+1+1} = 22.
MAPLE
b:= proc(n, i) option remember; local j; if n=0 then [1, 0] elif i<1
then [0$2] else b(n, i-1); for j to n/i do zip((x, y)->x+y, %,
[`if`(isprime(i), 0, NULL), b(n-i*j, i-1)[]], 0) od; %[1..2] fi
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..60); # Alois P. Heinz, May 29 2013
MATHEMATICA
zip = With[{m = Max[Length[#1], Length[#2]]}, PadRight[#1, m] + PadRight[#2, m]]&; b[n_, i_] := b[n, i] = Module[{j, pc}, Which[n == 0, {1, 0}, i<1, {0, 0}, True, pc = b[n, i-1]; For[j = 1, j <= n/i, j++, pc = zip[pc, Join[{If[PrimeQ[i], 0, Nothing]}, b[n-i*j, i-1]]] ]; pc[[1 ;; 2]] ]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 12 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 10 2007
STATUS
approved