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A103283 Triangle read by rows: T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n matrix with 2's on the diagonal and 1's elsewhere (n >= 1 and  0 <= k <= n). 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 (list; table; graph; refs; listen; history; text; internal format)
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 - 6*x^2 + 9*x - 4; so T(3,0) = -4, T(3,1) = 9, T(3,2) = -6, T(3,3) = 1.

Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:

   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.

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

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Last modified August 13 11:30 EDT 2022. Contains 356091 sequences. (Running on oeis4.)