A119493 - OEIS

%I #15 Aug 09 2015 15:29:48

%S 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,

%T 0,0,91050,0,-1350,8570,65392,0,187556,61650,0,-226,0,1402800,

%U -4810213,0,0,0,46764576,122333784,0,0,-82777822,-11359122,0,54911379,0,0

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

%C When is next nonzero value, for n>11?

%e a(3) = 0 because for instance, first row = 3rd row = (1,2,2).

%e a(6) = 0 because for instance, 3rd column = 6th column = (2,2,2,2,2,2).

%e a(7) = 0 because for instance, first column = 4th column.

%e a(9) = 0 because for instance, 9th column = 2 * 4th column.

%p From _R. J. Mathar_, Oct 15 2010: (Start)

%p read("transforms3") ; L := BFILETOLIST("b000002.txt") ;

%p 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)

%t 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 *)

%Y Cf. A000002.

%K easy,sign

%O 0,3

%A _Jonathan Vos Post_, May 25 2006

%E More terms from _R. J. Mathar_, Oct 15 2010