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).

1, -2, 1, 3, -5, 1, -4, 15, -8, 1, 5, -35, 36, -11, 1, -6, 70, -120, 66, -14, 1, 7, -126, 330, -286, 105, -17, 1, -8, 210, -792, 1001, -560, 153, -20, 1, 9, -330, 1716, -3003, 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

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 31 2006

Keywords

• sign
• tabl

Examples

			For n=5 the matrix is
+2 -1 +0 +0 +0
-3 +3 -1 +0 +0
+1 -3 +3 -1 +0
+0 +1 -3 +3 -1
+0 +0 +1 -3 +3
Triangle starts:
1,
-2, 1,
3, -5, 1,
-4, 15, -8, 1,
5, -35, 36, -11, 1,
-6, 70, -120, 66, -14, 1,
7, -126, 330, -286, 105, -17, 1,
		

Programs

Maple

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

Extensions

Edited by N. J. A. Sloane, Dec 03 2006