A089886 T(n,k) = number of subsets of {1,..., n} containing exactly k squares, triangle read by rows, 0<=k<n.

1, 2, 2, 4, 4, 0, 4, 8, 4, 0, 8, 16, 8, 0, 0, 16, 32, 16, 0, 0, 0, 32, 64, 32, 0, 0, 0, 0, 64, 128, 64, 0, 0, 0, 0, 0, 64, 192, 192, 64, 0, 0, 0, 0, 0, 128, 384, 384, 128, 0, 0, 0, 0, 0, 0, 256, 768, 768, 256, 0, 0, 0, 0, 0, 0, 0, 512, 1536, 1536, 512, 0, 0, 0, 0, 0, 0, 0, 0, 1024

Offset

1,2

Comments

T(n,k)=T(n, A000196(n)-k) for 0<=k<=A000196(n);

T(n,k)=0 iff k > A000196(n);

A089887(n)=T(n,0); A089889(n)=T(n,1) for n>1; A089890(n)=T(n,2) for n>2;

A089888(n) = Sum(T(n,k): 1<=k<=A000196(n));

T(n,k) = A007318(A000196(n),k)*A000079(n-A000196(n)).

Links

Table of n, a(n) for n=1..79.

Formula

T(n, k) = binomial(floor(n^(1/2)), k)*2^(n-floor(n^(1/2))).

Crossrefs

Cf. A000290.

Sequence in context: A323257 A054529 A074934 * A324648 A071511 A119922

Adjacent sequences: A089883 A089884 A089885 * A089887 A089888 A089889

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Nov 13 2003

Status

approved