A124019 - OEIS

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A124019

Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n band matrix with main diagonal 2,3,3,..., subdiagonal -3,-3,-3,..., sub-subdiagonal 1,1,1,... and superdiagonal -1,-1,-1,... (0<=k<=n).

1, -2, 1, 3, -5, 1, -4, 15, -8, 1, 5, -35, 36, -11, 1, -6, 70, -120, 66, -14, 1, 7, -126, 330, -286, 105, -17, 1, -8, 210, -792, 1001, -560, 153, -20, 1, 9, -330, 1716, -3003, 2380, -969, 210, -23, 1, -10, 495, -3432, 8008, -8568, 4845, -1540, 276, -26, 1, 11, -715, 6435, -19448, 27132, -20349, 8855, -2300, 351, -29, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

For n=5 the matrix is

+2 -1 +0 +0 +0

-3 +3 -1 +0 +0

+1 -3 +3 -1 +0

+0 +1 -3 +3 -1

+0 +0 +1 -3 +3

Triangle starts:

-2, 1,

3, -5, 1,

-4, 15, -8, 1,

5, -35, 36, -11, 1,

-6, 70, -120, 66, -14, 1,

7, -126, 330, -286, 105, -17, 1,

MAPLE

with(linalg): m:=proc(i, j) if i=1 and j=1 then 2 elif i=j then 3 elif j-i=1 then -1 elif i-j=1 then -3 elif i-j=2 then 1 else 0 fi end: T:=proc(n, k) if n=0 and k=0 then 1 elif n>0 and k<=n then coeff(charpoly(matrix(n, n, m), x), x, k) else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

CROSSREFS

Sequence in context: A119308 A110197 A124819 * A337886 A337884 A337883

Adjacent sequences: A124016 A124017 A124018 * A124020 A124021 A124022

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 31 2006

EXTENSIONS

Edited by N. J. A. Sloane, Dec 03 2006

STATUS

approved