%I
%S 1,3,1,8,6,1,20,24,9,1,48,80,48,12,1,112,240,200,80,15,1,256,
%T 672,720,400,120,18,1,576,1792,2352,1680,700,168,21,1,1280,
%U 4608,7168,6272,3360,1120,224,24,1,2816,11520,20736,21504,14112,6048,1680,288,27,1,6144,28160,57600,69120
%N Triangle read by rows: T(n,k) is the coefficient of x^k (0<=k<=n) in the monic characteristic polynomial of the n X n matrix with 3's on the diagonal and 1's elsewhere (n>=1). Row 0 consists of the single term 1.
%C Row sums of the unsigned triangle yield A006234. The unsigned triangle is the mirror image of A103407.
%F Appears to be the matrix product (IS)*P^(2), where I is the identity, P is Pascal's triangle A007318 and S is A132440, the infinitesimal generator of P. Cf. A055137 (= (IS)*P) and A103283 (= (IS)*P^(1)).  _Peter Bala_, Nov 28 2011
%e The monic characteristic polynomial of the matrix [3 1 1 / 1 3 1 / 1 1 3] is x^3  9x^2 + 24x  20; so T(3,0)=20, T(3,1)=24, T(3,2)=9, T(3,3)=1.
%e Triangle begins:
%e 1;
%e 3,1;
%e 8,6,1;
%e 20,24,9,1;
%e 48,80,48,12,1;
%p with(linalg): a:=proc(i,j) if i=j then 3 else 1 fi end: 1;for n from 1 to 10 do seq(coeff(expand(x*charpoly(matrix(n,n,a),x)),x^k),k=1..n+1) od; # yields the sequence in triangular form
%Y Cf. A006234, A103407.
%K sign,tabl
%O 0,2
%A _Emeric Deutsch_, Mar 19 2005
