A107430 Triangle read by rows: row n is row n of Pascal's triangle (A007318) sorted into increasing order.
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 6, 1, 1, 5, 5, 10, 10, 1, 1, 6, 6, 15, 15, 20, 1, 1, 7, 7, 21, 21, 35, 35, 1, 1, 8, 8, 28, 28, 56, 56, 70, 1, 1, 9, 9, 36, 36, 84, 84, 126, 126, 1, 1, 10, 10, 45, 45, 120, 120, 210, 210, 252, 1, 1, 11, 11, 55, 55, 165, 165, 330, 330, 462, 462, 1
Offset: 0
Examples
Triangle begins: 1; 1,1; 1,1,2; 1,1,3,3; 1,1,4,4,6;
Links
Crossrefs
A061554 is similar but with rows sorted into decreasing order.
Cf. A034868.
Cf. A053121. - Gary W. Adamson, Dec 28 2008
Cf. A103284.
Programs
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Haskell
import Data.List (sort) a107430 n k = a107430_tabl !! n !! k a107430_row n = a107430_tabl !! n a107430_tabl = map sort a007318_tabl -- Reinhard Zumkeller, May 26 2013
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Magma
/* As triangle */ [[Binomial(n,Floor(k/2)) : k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Sep 22 2015
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Maple
for n from 0 to 10 do sort([seq(binomial(n,k),k=0..n)]) od; # yields sequence in triangular form. - Emeric Deutsch, May 28 2005
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Mathematica
Flatten[ Table[ Sort[ Table[ Binomial[n, k], {k, 0, n}]], {n, 0, 12}]] (* Robert G. Wilson v, May 28 2005 *) -
PARI
for(n=0,20, for(k=0,n, print1(binomial(n,floor(k/2)), ", "))) \\ G. C. Greubel, May 22 2017
Formula
T(n,k) = C(n,floor(k/2)). - Paul Barry, Dec 15 2006; corrected by Philippe Deléham, Mar 15 2007
Extensions
More terms from Emeric Deutsch and Robert G. Wilson v, May 28 2005
Comments