A070543 Triangular array read by rows: T(n,k) = number of k-dimensional isotropic subspaces of Spin(2n+1,C), n >= 1, 1 <= k <= n.

1, 3, 3, 5, 7, 6, 7, 11, 12, 10, 9, 15, 18, 18, 15, 11, 19, 24, 26, 25, 21, 13, 23, 30, 34, 35, 33, 28, 15, 27, 36, 42, 45, 45, 42, 36, 17, 31, 42, 50, 55, 57, 56, 52, 45, 19, 35, 48, 58, 65, 69, 70, 68, 63, 55, 21, 39, 54, 66, 75, 81, 84, 84, 81, 75, 66, 23, 43, 60, 74, 85, 93

Offset: 1

Author

Michael Somos, Apr 28 2002

Keywords

• nonn
• tabl
• easy
• nice

Examples

			Rows:
   1;
   3,  3;
   5,  7,  6;
   7, 11, 12, 10;
   9, 15, 18, 18, 15;
  11, 19, 24, 26, 25, 21;
  ...
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened
• John Baez, Week 181

Crossrefs

Cf. A141419.

Programs

GAP

Flat(List([1..12], n-> List([1..n], k-> k*(k+1 + 4*(n-k))/2 ))); # G. C. Greubel, Sep 05 2019

Magma

[k*(k+1 + 4*(n-k))/2: k in [1..n], n in [1..12]]; // G. C. Greubel, Sep 05 2019

Maple

T:=(n,k) -> k*(k+1)/2+2*k*(n-k); r:=n->[seq(T(n,k),k=1..n)]; for r from 1 to 12 do lprint(r(n)); od: # N. J. A. Sloane, Aug 21 2019

Mathematica

nmax = 12; t[n_, k_] := If[k < 1 || k > n, 0, k*(k+1)/2 + 2*k*(n-k)]; Flatten[ Table[t[n , k], {n, 1, nmax}, {k, 1, n}]] (* Jean-François Alcover, Oct 19 2011, after PARI *)

PARI

{T(n, k) = if( k<1 || k>n, 0, k * (k + 1) / 2 + 2 * k * (n - k))}

Sage

[[k*(k+1 + 4*(n-k))/2 for k in (1..n)] for n in (1..12)] # G. C. Greubel, Sep 05 2019

Formula

T(n, k) = k*(k+1)/2 + 2*k*(n-k) if 0 < k <= n.

G.f.: (1+x-2*x^2*y)/((1-x)^2*(1-x*y)^3). - Vladeta Jovovic, Mar 05 2004

T(n, k) = A141419(2*n-k, k). - Peter Munn, Aug 21 2019

Extensions

Offset changed to 1 by N. J. A. Sloane, Aug 21 2019