cp's OEIS Frontend

A124019 Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n band matrix with main diagonal 2,3,3,..., subdiagonal -3,-3,-3,..., sub-subdiagonal 1,1,1,... and superdiagonal -1,-1,-1,... (0<=k<=n).

%I A124019 #8 Oct 09 2012 04:03:40
%S A124019 1,-2,1,3,-5,1,-4,15,-8,1,5,-35,36,-11,1,-6,70,-120,66,-14,1,7,-126,
%T A124019 330,-286,105,-17,1,-8,210,-792,1001,-560,153,-20,1,9,-330,1716,-3003,
%U A124019 2380,-969,210,-23,1,-10,495,-3432,8008,-8568,4845,-1540,276,-26,1,11,-715,6435,-19448,27132,-20349,8855,-2300,351,-29,1
%N A124019 Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n band matrix with main diagonal 2,3,3,..., subdiagonal -3,-3,-3,..., sub-subdiagonal 1,1,1,... and superdiagonal -1,-1,-1,... (0<=k<=n).
%e A124019 For n=5 the matrix is
%e A124019 +2 -1 +0 +0 +0
%e A124019 -3 +3 -1 +0 +0
%e A124019 +1 -3 +3 -1 +0
%e A124019 +0 +1 -3 +3 -1
%e A124019 +0 +0 +1 -3 +3
%e A124019 Triangle starts:
%e A124019 1,
%e A124019 -2, 1,
%e A124019 3, -5, 1,
%e A124019 -4, 15, -8, 1,
%e A124019 5, -35, 36, -11, 1,
%e A124019 -6, 70, -120, 66, -14, 1,
%e A124019 7, -126, 330, -286, 105, -17, 1,
%p A124019 with(linalg): m:=proc(i,j) if i=1 and j=1 then 2 elif i=j then 3 elif j-i=1 then -1 elif i-j=1 then -3 elif i-j=2 then 1 else 0 fi end: T:=proc(n,k) if n=0 and k=0 then 1 elif n>0 and k<=n then coeff(charpoly(matrix(n,n,m),x),x,k) else 0 fi end: for n from 0 to 10 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
%K A124019 sign,tabl
%O A124019 0,2
%A A124019 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 31 2006
%E A124019 Edited by _N. J. A. Sloane_, Dec 03 2006