A089052 Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) = number of partitions of n into exactly k powers of 2.

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 1, 2, 2, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 3, 3, 2, 2, 2, 1, 1, 1

Offset

0,25

References

J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013

Links

Alois P. Heinz, Rows n = 0..200, flattened

J. Jordan and R. Southwell, Further Properties of Reproducing Graphs, Applied Mathematics, Vol. 1 No. 5, 2010, pp. 344-350. doi: 10.4236/am.2010.15045. - From N. J. A. Sloane, Feb 03 2013

Formula

T(2m, k) = T(m, k)+T(2m-1, k-1); T(2m+1, k) = T(2m, k-1).

G.f.: 1/Product_{k>=0} (1-y*x^(2^k)). - Vladeta Jovovic, Dec 03 2003

Example

1
0 1
0 1 1
0 0 1 1
0 1 1 1 1
0 0 1 1 1 1
0 0 1 2 1 1 1
0 0 0 1 2 1 1 1
0 1 1 1 2 2 1 1 1
0 0 1 1 1 2 2 1 1 1
0 0 1 2 2 2 2 2 1 1 1
0 0 0 1 2 2 2 2 2 1 1 1

Maple

A089052 := proc(n, k)
    option remember;
    if k > n then
        return(0);
    end if;
    if k= 0 then
        if n=0 then
            return(1)
        else
            return(0);
        end if;
    end if;
    if n mod 2 = 1 then
            return procname(n-1, k-1);
    end if;
    procname(n-1, k-1)+procname(n/2, k);
end proc:

Mathematica

t[n_, k_] := t[n, k] = Which[k > n, 0, k == 0, If[n == 0, 1, 0], Mod[n, 2] == 1, t[n-1, k-1], True, t[n-1, k-1] + t[n/2, k]]; Table[t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014, after Maple *)

Crossrefs

Columns give A036987, A075897 (essentially), A089049, A089050, A089051, A319922.

Row sums give A018819.

See A089053 for another version.

Sequence in context: A176724 A015318 A026836 * A284606 A284019 A286135

Adjacent sequences: A089049 A089050 A089051 * A089053 A089054 A089055

Keyword

nonn,tabl

Author

N. J. A. Sloane, Dec 03 2003

Status

approved