The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A157000

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A157000

Triangle T(n,k) = (n/k)*binomial(n-k-1, k-1) read by rows.
(history; published version)

#25 by Charles R Greathouse IV at Thu Sep 08 08:45:41 EDT 2022

PROG

(MAGMAMagma) [[n*Binomial(n-k-1, k-1)/k: k in [1..Floor(n/2)]]: n in [2..20]]; // G. C. Greubel, Apr 25 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#24 by Susanna Cuyler at Thu Apr 25 22:41:42 EDT 2019

STATUS

proposed

approved

#23 by G. C. Greubel at Thu Apr 25 16:30:47 EDT 2019

STATUS

editing

proposed

#22 by G. C. Greubel at Thu Apr 25 16:30:09 EDT 2019

DATA

2, 3, 4, 2, 5, 5, 6, 9, 2, 7, 14, 7, 8, 20, 16, 2, 9, 27, 30, 9, 10, 35, 50, 25, 2, 11, 44, 77, 55, 11, 12, 54, 112, 105, 36, 2, 13, 65, 156, 182, 91, 13, 14, 77, 210, 294, 196, 49, 2, 15, 90, 275, 450, 378, 140, 15, 16, 104, 352, 660, 672, 336, 64, 2, 17, 119, 442, 935, 1122, 714, 204, 17

LINKS

G. C. Greubel, <a href="/A157000/b157000.txt">Rows n = 2..100 of triangle, flattened</a>

EXAMPLE

2;

3;

4, 2;

5, 5;

6, 9, 2;

7, 14, 7;

8, 20, 16, 2;

9, 27, 30, 9;

10, 35, 50, 25, 2;

11, 44, 77, 55, 11;

12, 54, 112, 105, 36, 2;

MATHEMATICA

gTable[n_, k_] := (n/k)*Binomial[n - k - 1, k - 1]; , {n, 2, 20}, {k, 1, Floor[n/2]}]//Flatten (* modified by _G. C. Greubel_, Apr 25 2019 *)

Table[Table[g[n, k + 1], {k, 0, Floor[n/2] - 1}], {n, 12}];

Flatten[%]

PROG

(MAGMA) [[n*Binomial(n-k-1, k-1)/k: k in [1..Floor(n/2)]]: n in [2..20]]; // G. C. Greubel, Apr 25 2019

(Sage) [[n*binomial(n-k-1, k-1)/k for k in (1..floor(n/2))] for n in (2..20)] # G. C. Greubel, Apr 25 2019

STATUS

approved

editing

#21 by N. J. A. Sloane at Sun Mar 02 14:39:08 EST 2014

STATUS

proposed

approved

#20 by Wesley Ivan Hurt at Sun Mar 02 13:14:23 EST 2014

STATUS

editing

proposed

Discussion

Sun Mar 02

13:28

Michel Marcus: Bert, to sign , use ~~~~ : it will be converted into name+ date in correct format. Thanks.

#19 by Wesley Ivan Hurt at Sun Mar 02 13:11:38 EST 2014

COMMENTS

T(n,k) is the number of ways to select k knights from a round table of n knights, no two adjacent. - Bert Seghers, Mar 02 2014

FORMULA

T(n,k) = binomial(n-k,k) + binomial(n-k-1,k-1). - Bert Seghers, Mar 02 2014

STATUS

proposed

editing

#18 by Joerg Arndt at Sun Mar 02 12:44:47 EST 2014

STATUS

editing

proposed

#17 by Joerg Arndt at Sun Mar 02 12:44:28 EST 2014

FORMULA

T(n,k) = binomial(n-k,k) + binomial(n-k-1,k-1). - _Bert Seghers_, Mar 2014

PROG

(PARI) a(n, k)=n*binomial(n-k-1, k-1)/k ; \\ Charles R Greathouse IV, Jul 10 2011

STATUS

proposed

editing

#16 by Michel Marcus at Sun Mar 02 11:47:18 EST 2014

STATUS

editing

proposed