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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 (list; table; graph; refs; listen; history; text; internal format)
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 (I-S)*P^(-2), where I is the identity, P is Pascal's triangle A007318 and S is A132440, the infinitesimal generator of P. Cf. A055137 (= (I-S)*P) and A103283 (= (I-S)*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

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Last modified May 25 11:17 EDT 2019. Contains 323539 sequences. (Running on oeis4.)