

A103283


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 2's on the diagonal and 1's elsewhere (n>=1). Row 0 consists of the single term 1.


4



1, 2, 1, 3, 4, 1, 4, 9, 6, 1, 5, 16, 18, 8, 1, 6, 25, 40, 30, 10, 1, 7, 36, 75, 80, 45, 12, 1, 8, 49, 126, 175, 140, 63, 14, 1, 9, 64, 196, 336, 350, 224, 84, 16, 1, 10, 81, 288, 588, 756, 630, 336, 108, 18, 1, 11, 100, 405, 960, 1470, 1512, 1050, 480, 135, 20, 1, 12, 121, 550, 1485, 2640
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..70.


EXAMPLE

The monic characteristic polynomial of the matrix [2 1 1 / 1 2 1 / 1 1 2] is x^3  6x^2 + 9x  4; so T(3,0)=4, T(3,1)=9, T(3,2)=6, T(3,3)=1.
Triangle begins:
1;
2,1;
3,4,1;
4,9,6,1;
5,16,18,8,1;


MAPLE

with(linalg): a:=proc(i, j) if i=j then 2 else 1 fi end: 1; for n from 1 to 11 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

Row sums yield the sequence 1, 1, 0, 0, 0, ... . Row sums of the unsigned triangle yield A001792. See A093375 for a signed version. A103406 is a mirror image.
Cf. A001792.
Sequence in context: A133807 A325001 A093375 * A104698 A067066 A210219
Adjacent sequences: A103280 A103281 A103282 * A103284 A103285 A103286


KEYWORD

sign,tabl


AUTHOR

Gary W. Adamson, Feb 04 2005


EXTENSIONS

Edited by Emeric Deutsch, Mar 19 2005


STATUS

approved



