login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184173 Triangle read by rows: T(n,k) is the sum of the k X k minors in the n X n Pascal matrix (0<=k<=n; the empty 0 X 0 minor is defined to be 1). 0
1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 34, 15, 1, 1, 31, 144, 144, 31, 1, 1, 63, 574, 1155, 574, 63, 1, 1, 127, 2226, 8526, 8526, 2226, 127, 1, 1, 255, 8533, 60588, 113832, 60588, 8533, 255, 1, 1, 511, 32587, 424117, 1444608, 1444608, 424117, 32587, 511, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Apparently, the sum of the entries in row n is A005157(n).

LINKS

Alois P. Heinz, Rows n = 0..12, flattened

Wikipedia, Minor (linear algebra)

FORMULA

The triangle is symmetric: T(n,k) = T(n,n-k).

EXAMPLE

T(3,1) = 7 because in the 3 X 3 Pascal matrix [1,0,0/1,1,0/1,2,1] the sum of the entries is 7.

Triangle starts:

  1;

  1,  1;

  1,  3,  1;

  1,  7,  7,  1;

  1, 15, 34, 15, 1;

MAPLE

with(combinat): with(LinearAlgebra):

T:= proc(n, k) option remember; `if`(n-k<k, T(n, n-k), (l-> add(add(

      Determinant(SubMatrix(Matrix(n, (i, j)-> binomial(i-1, j-1)),

       i, j)), j in l), i in l))(choose([$1..n], k)))

    end:

seq(seq(T(n, k), k=0..n), n=0..7);  # Alois P. Heinz, Feb 11 2019

CROSSREFS

Columns k=0-2 give: A000012, A000225, A306376.

Cf. A005157, A007318.

Sequence in context: A157152 A136126 A046802 * A022166 A141689 A058669

Adjacent sequences:  A184170 A184171 A184172 * A184174 A184175 A184176

KEYWORD

nonn,tabl,changed

AUTHOR

Emeric Deutsch, Jan 12 2011

EXTENSIONS

Typo corrected by Alois P. Heinz, Feb 11 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)