

A103247


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.


5



1, 3, 1, 8, 6, 1, 20, 24, 9, 1, 48, 80, 48, 12, 1, 112, 240, 200, 80, 15, 1, 256, 672, 720, 400, 120, 18, 1, 576, 1792, 2352, 1680, 700, 168, 21, 1, 1280, 4608, 7168, 6272, 3360, 1120, 224, 24, 1, 2816, 11520, 20736, 21504, 14112, 6048, 1680, 288, 27, 1, 6144, 28160, 57600, 69120
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OFFSET

0,2


COMMENTS

Row sums of the unsigned triangle yield A006234. The unsigned triangle is the mirror image of A103407.


LINKS

Table of n, a(n) for n=0..58.


FORMULA

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


EXAMPLE

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.
Triangle begins:
1;
3,1;
8,6,1;
20,24,9,1;
48,80,48,12,1;


MAPLE

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


CROSSREFS

Cf. A006234, A103407.
Sequence in context: A258018 A188939 A062196 * A030523 A207815 A125662
Adjacent sequences: A103244 A103245 A103246 * A103248 A103249 A103250


KEYWORD

sign,tabl


AUTHOR

Emeric Deutsch, Mar 19 2005


STATUS

approved



