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A102366 Number of subsets of {1,2,...,n} in which exactly half of the elements are less than or equal to sqrt(n). 0
1, 1, 2, 3, 6, 10, 15, 21, 28, 84, 120, 165, 220, 286, 364, 455, 1820, 2380, 3060, 3876, 4845, 5985, 7315, 8855, 10626, 53130, 65780, 80730, 98280, 118755, 142506, 169911, 201376, 237336, 278256, 324632, 1947792, 2324784, 2760681, 3262623, 3838380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(n) = Sum_k C(floor(sqrt(n)), k)*C(n-floor(sqrt(n)), k) = A048093(n)+1 = a(n-1)+A084919(n-1)

a(n) = binomial(n, floor(sqrt(n))). [From Paul D. Hanna, Jun 25 2011]

EXAMPLE

a(5)=10 since the ten subsets of {1,2,3,4,5} are { }, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {1,2, 3,4}, {1,2, 3,5} and {1,2, 4,5}.

PROG

(PARI) {a(n)=if(n<0, 0, binomial(n, sqrtint(n)))} /* Paul D. Hanna */

(PARI) {a(n)=sum(k=0, sqrtint(n), binomial(sqrtint(n), k)*binomial(n-sqrtint(n), k))}

CROSSREFS

Cf. A011782 for number of subsets with an even number of elements.

Sequence in context: A111467 A215891 A254033 * A152452 A217741 A074134

Adjacent sequences:  A102363 A102364 A102365 * A102367 A102368 A102369

KEYWORD

nonn

AUTHOR

Henry Bottomley, Feb 22 2005

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)