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A357812

Number of subsets of [n] in which exactly half of the elements are powers of 2.

1, 1, 1, 3, 4, 10, 20, 35, 70, 126, 210, 330, 495, 715, 1001, 1365, 4368, 6188, 8568, 11628, 15504, 20349, 26334, 33649, 42504, 53130, 65780, 80730, 98280, 118755, 142506, 169911, 906192, 1107568, 1344904, 1623160, 1947792, 2324784, 2760681, 3262623, 3838380

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = binomial(n,A029837(n+1)).

a(n) = binomial(n,A113473(n)) for n>0, a(0) = 1.

a(n) = Sum_{j>=0} binomial(A029837(n+1),j)*binomial(n-A029837(n+1),j).

EXAMPLE

a(6) = 20: {}, {1,3}, {1,5}, {1,6}, {2,3}, {2,5}, {2,6}, {3,4}, {4,5}, {4,6}, {1,2,3,5}, {1,2,3,6}, {1,2,5,6}, {1,3,4,5}, {1,3,4,6}, {1,4,5,6}, {2,3,4,5}, {2,3,4,6}, {2,4,5,6}, {1,2,3,4,5,6}.

MAPLE

a:= n-> binomial(n, max(0, 1+ilog[2](n))):

seq(a(n), n=0..40);

PROG

(Python)

from math import comb

def A357812(n): return comb(n, n.bit_length()) # Chai Wah Wu, Oct 14 2022

CROSSREFS

Cf. A000079, A029837, A037031, A102366, A113473, A180272, A357927.

Sequence in context: A345322 A255539 A326832 * A321197 A109887 A200981

Adjacent sequences: A357809 A357810 A357811 * A357813 A357814 A357815

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 13 2022

STATUS

approved

URL: https://oeis.org/A357812

⇱ A357812 - OEIS