A225860 Number of partitions of 2^n into binomial coefficients C(n,k).

1, 1, 3, 3, 10, 16, 55, 133, 599, 1956, 11982, 57872, 477289, 3290993, 37671322, 373566217, 5986589127, 85738839408, 1931359427404, 40003346563574, 1274368885871702, 38222180804346119, 1729302096638372691, 75195441157176495562, 4848355840082055530710

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Example

n=3: C(3,0)=C(3,3) = 1, C(3,1)=C(3,2) = 3, 2^3 = 8:
a(3) = #{3+3+1+1, 3+1+1+1+1+1, 8x1} = 3;
n=4: C(4,0)=C(4,4) = 1, C(4,1)=C(4,3) = 4, C(4,2) = 6, 2^4 = 16:
a(4) = #{6+6+4, 6+6+1+1+1+1, 6+4+4+1+1, 6+4+6x1, 6+10x1, 4+4+4+4, 4+4+4+1+1+1+1, 4+4+8x1, 4+12x1, 16x1} = 10
n=5: C(5,0)=C(5,5) = 1, C(5,1)=C(5,4) = 5, C(5,2)=C(5,3) = 10, 2^5 = 32:
a(5) = #{10+10+10+1+1, 10+10+5+5+1+1, 10+10+5+7x1, 10+10+12x1, 10+5+5+5+5+1+1, 10+5+5+5+7x1, 10+5+5+12x1, 10+5+17x1, 10+22x1, 6x5, 5x5+7x1, 5+5+5+5+12x1, 5+5+5+17x1, 5+5+22x1, 5+27x1, 32x1} = 16.

Maple

a:= proc(n) option remember; local g, i, j, l, m, t;
      m:= 1+iquo(n, 2);
      l:= array(1..m, [seq(binomial(n, k), k=0..m-1)]);
      g:= array(1..m, [seq(array(0..l[i]-1, [0$(l[i])]), i=1..m)]);
      g[1][0]:= 1;
      for j from 0 to 2^n do for i from 2 to m do
        g[i][irem(j, l[i])]:= g[i][irem(j, l[i])]
                             +g[i-1][irem(j, l[i-1])]
      od od; g[m][irem(2^n, l[m])]
    end:
seq(a(n), n=0..14);  # Alois P. Heinz, May 30 2013

Prog

(Haskell)
a225860 n = p (a034868_row n) (2 ^ n) where
   p _          0 = 1
   p []         _ = 0
   p bs'@(b:bs) m = if m < b then 0 else p bs' (m - b) + p bs m

Crossrefs

Cf. A000079, A034868, A007318.

Sequence in context: A262923 A367301 A319882 * A024313 A132331 A077899

Adjacent sequences: A225857 A225858 A225859 * A225861 A225862 A225863

Keyword

nonn

Author

Reinhard Zumkeller, May 26 2013

Extensions

a(13)-a(23) from Alois P. Heinz, May 30 2013

a(24) from Alois P. Heinz, Oct 06 2014

Status

approved