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A157000 Triangle T(n,k) = (n/k)*binomial(n-k-1, k-1) read by rows. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row sums are A001610(n-1).

Triangle A034807 (coefficients of Lucas polynomials) with the first column omitted. - Philippe Deléham, Mar 17 2013

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

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 199

LINKS

Table of n, a(n) for n=2..71.

FORMULA

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

EXAMPLE

The table starts in row n=2, column k=1 as:

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

g[n_, k_] := (n/k)*Binomial[n - k - 1, k - 1];

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

Flatten[%]

PROG

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

CROSSREFS

Cf. A132460, A113279, A082985, A029635.

Sequence in context: A260643 A243849 A286547 * A026346 A295887 A293450

Adjacent sequences:  A156997 A156998 A156999 * A157001 A157002 A157003

KEYWORD

nonn,easy,tabf

AUTHOR

Roger L. Bagula, Feb 20 2009

EXTENSIONS

Offset 2, keyword:tabf, more terms by the Assoc. Eds. of the OEIS, Nov 01 2010

STATUS

approved

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Last modified February 20 02:47 EST 2018. Contains 299357 sequences. (Running on oeis4.)