A071223 -id:A071223 - cp's OEIS frontend

A087645 Third column of A071223.

2, 6, 24, 72, 172, 352, 646, 1094, 1742, 2642, 3852, 5436, 7464, 10012, 13162, 17002, 21626, 27134, 33632, 41232, 50052, 60216, 71854, 85102, 100102, 117002, 135956, 157124, 180672, 206772, 235602, 267346, 302194, 340342, 381992, 427352, 476636

Offset: 2

N. J. A. Sloane, Oct 26 2003

Colin Barker, Table of n, a(n) for n = 2..1000
Alvaro Carbonero, Beth Anne Castellano, Gary Gordon, Charles Kulick, Karie Schmitz, and Brittany Shelton, Permutations of point sets in R_d, arXiv:2106.14140 [math.CO], 2021.
T. M. Cover, The number of linearly inducible orderings of points in d-space, SIAM J. Applied Math., 15 (1967), 434-439.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A052149, A071223.

CoefficientList[Series[-2 x^2*(x^4 - 4 x^3 + 7 x^2 - 2 x + 1)/(x - 1)^5, {x, 0, 38}], x][[3 ;; -1]] (* Michael De Vlieger, Oct 19 2021 *)

Vec(-2*x^2*(x^4-4*x^3+7*x^2-2*x+1)/(x-1)^5 + O(x^100)) \\ Colin Barker, Dec 06 2014

a(n) = A052149(n+1) + 2.
a(n) = (3*n^4-10*n^3+9*n^2-2*n+24)/12. - Vladeta Jovovic, Oct 26 2003
G.f.: -2*x^2*(x^4-4*x^3+7*x^2-2*x+1) / (x-1)^5. - Colin Barker, Dec 06 2014

More terms from Vladeta Jovovic, Oct 26 2003

A198889 Square array in A071223 read by antidiagonals.

Original entry on oeis.org

2, 2, 2, 2, 6, 2, 2, 12, 6, 2, 2, 20, 24, 6, 2, 2, 30, 72, 24, 6, 2, 2, 42, 172, 120, 24, 6, 2, 2, 56, 352, 480, 120, 24, 6, 2, 2, 72, 646, 1512, 720, 120, 24, 6, 2, 2, 90, 1094, 3976, 3600, 720, 120, 24, 6, 2, 2, 110, 1742, 9144, 14184, 5040, 720, 120, 24, 6, 2, 2, 132, 2642, 18990, 45992, 30240, 5040, 720, 120

Offset: 2

N. J. A. Sloane, Oct 30 2011

			Array begins
  2  2   2   2   2  ...
  2  6   6   6   6 ...
  2 12  24  24  24 ...
  2 20  72 120 120 ...
  2 30 172 480 720 ...
  ...

T. M. Cover, The number of linearly inducible orderings of points in d-space, SIAM J. Applied Math., 15 (1967), 434-439.

Cf. A071223.

A071223 := proc(n,k)
        if k=1 and n>=2 then
                2
        elif n=2 and k>=1 then
                2
        elif k>=n-1 then
                n!
        else
        procname(n-1, k)+(n-1)*procname(n-1, k-1)
        fi ;
end proc:
for d from 3 to 16 do
        for k from 1 to d-2 do
                n := d-k ;
                printf("%d,",A071223(n,k)) ;
        end do:
end do; # R. J. Mathar, Oct 31 2011

See A071223, which is the main entry for this array.

A087644 Triangle T(n,k) (n >= 2, 1 <= k <= n) read by rows: (1/2) times number of linearly inducible orderings of n points in k-dimensional Euclidean space.

Original entry on oeis.org

1, 1, 3, 1, 6, 12, 1, 10, 36, 60, 1, 15, 86, 240, 360, 1, 21, 176, 756, 1800, 2520, 1, 28, 323, 1988, 7092, 15120, 20160, 1, 36, 547, 4572, 22996, 71856, 141120, 181440, 1, 45, 871, 9495, 64144, 278820, 787824, 1451520, 1814400, 1, 55, 1321, 18205, 159094

Offset: 2

N. J. A. Sloane, Oct 26 2003

Equals A071223/2. See that entry for further information.

T. M. Cover, The number of linearly inducible orderings of points in d-space, SIAM J. Applied Math., 15 (1967), 434-439.

Cf. A071223.

T:=proc(n,k) if k>=n then 0 elif k=1 and n>=2 then 1 elif n=2 and k>=1 then 1 elif k=n-1 then n!/2 else T(n-1,k)+(n-1)*T(n-1,k-1) fi end:seq(seq(T(n,k),k=1..n-1),n=2..12);

More terms from Emeric Deutsch, May 24 2004

cp's OEIS Frontend

A087645 Third column of A071223.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A198889 Square array in A071223 read by antidiagonals.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Formula

A087644 Triangle T(n,k) (n >= 2, 1 <= k <= n) read by rows: (1/2) times number of linearly inducible orderings of n points in k-dimensional Euclidean space.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Extensions