The On-Line Encyclopedia of Integer Sequences (OEIS)

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A089886

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

#5 by Russ Cox at Fri Mar 30 18:50:42 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Nov 13 2003

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,tabl,new

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Nov 13 2003

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

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

KEYWORD

nonn,tabl,new

#2 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

COMMENTS

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

KEYWORD

nonn,tabl,new

#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

NAME

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

DATA

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)).

FORMULA

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

CROSSREFS

Cf. A000290.

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 13 2003

STATUS

approved