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

Author

Philippe Deléham, May 21 2005

Keywords

• nonn
• tabl
• easy

Comments

By rows, equals partial sums of A053121 reversed rows. Example: Row 4 of A053121 = (2, 0, 3, 0, 1) -> (1, 0, 3, 0, 2) -> (1, 1, 4, 4, 6). - Gary W. Adamson, Dec 28 2008, edited by Michel Marcus, Sep 22 2015

Examples

			Triangle begins:
1;
1,1;
1,1,2;
1,1,3,3;
1,1,4,4,6;
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

A061554 is similar but with rows sorted into decreasing order.

Cf. A034868.

Cf. A053121. - Gary W. Adamson, Dec 28 2008

Cf. A103284.

Programs

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

Magma

/* As triangle */ [[Binomial(n,Floor(k/2)) : k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Sep 22 2015

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

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

Sum_{k=0..n} T(n,k)*x^(n-k) = A127363(n), A127362(n), A127361(n), A126869(n), A001405(n), A000079(n), A127358(n), A127359(n), A127360(n) for x=-4,-3,-2,-1,0,1,2,3,4 respectively. - Philippe Deléham, Mar 29 2007

Extensions

More terms from Emeric Deutsch and Robert G. Wilson v, May 28 2005