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

0,6

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

Links

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

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

Example

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

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 *)

Prog

(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
(PARI) for(n=0, 20, for(k=0, n, print1(binomial(n, floor(k/2)), ", "))) \\ G. C. Greubel, May 22 2017

Crossrefs

A061554 is similar but with rows sorted into decreasing order.

Cf. A034868.

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

Cf. A103284.

Sequence in context: A176427 A324592 A099573 * A330885 A355146 A255741

Adjacent sequences: A107427 A107428 A107429 * A107431 A107432 A107433

Keyword

nonn,tabl,easy

Author

Philippe Deléham, May 21 2005

Extensions

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

Status

approved