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A225860 Number of partitions of 2^n into binomial coefficients C(n,k). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A330288 A262923 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

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Last modified July 14 13:27 EDT 2020. Contains 335729 sequences. (Running on oeis4.)