A119493 Determinant of n X n matrix of first n^2 terms of Kolakoski sequence (A000002).

0, 1, -3, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 140, 0, 0, 0, 0, 0, -205, 0, -44, 0, 0, 0, 0, 0, 0, 91050, 0, -1350, 8570, 65392, 0, 187556, 61650, 0, -226, 0, 1402800, -4810213, 0, 0, 0, 46764576, 122333784, 0, 0, -82777822, -11359122, 0, 54911379, 0, 0

Offset: 0

Author

Jonathan Vos Post, May 25 2006

Keywords

• easy
• sign

Comments

When is next nonzero value, for n>11?

Examples

			a(3) = 0 because for instance, first row = 3rd row = (1,2,2).
a(6) = 0 because for instance, 3rd column = 6th column = (2,2,2,2,2,2).
a(7) = 0 because for instance, first column = 4th column.
a(9) = 0 because for instance, 9th column = 2 * 4th column.
		

Crossrefs

Cf. A000002.

Programs

Maple

From R. J. Mathar, Oct 15 2010: (Start)
read("transforms3") ; L := BFILETOLIST("b000002.txt") ;
for s from 1 to floor(sqrt(nops(L))) do m := Matrix(1..s,1..s) ; for r from 0 to s-1 do for c from 0 to s-1 do m[r+1,c+1] := op(1+c+r*s,L) ; end do: end do: printf("%a,\n", LinearAlgebra[Determinant](m) ) ; end do: (End)

Mathematica

nmax = 56; a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1 + Mod[n-1, 2]}], {n, 3, nmax^2}, {a2[[n]]}]; a[0] = 0; a[n_] := Det[ Partition[ Take[a2, n^2], n]]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jun 18 2013 *)

Extensions

More terms from R. J. Mathar, Oct 15 2010