A136644 Triangle of coefficients of characteristic polynomials of asymmetrical tridiagonal matrices: Middle diagonal: a=1; Lower first subdiagonal: b=2; Upper first subdiagonal: c=1; Example: M(3) {{1, 1, 0}, {2, 1, 1}, {0, 2, 1}}.

1, 1, -1, -1, -2, 1, -3, 1, 3, -1, -1, 8, 0, -4, 1, 5, 7, -14, -2, 5, -1, 7, -14, -21, 20, 5, -6, 1, -3, -35, 21, 45, -25, -9, 7, -1, -17, -4, 98, -16, -80, 28, 14, -8, 1, -11, 83, 60, -204, -14, 126, -28, -20, 9, -1, 23, 102, -219, -232, 350, 84, -182, 24, 27, -10, 1

Offset

1,5

Comments

Row sums are:

{1, 0, -2, 0, 4, 0, -8, 0, 16, 0, -32}

References

Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 516.

Links

Table of n, a(n) for n=1..66.

Formula

a(n)= 1; b(n)= 2; c(n) = 1; T(n, m, d) := If[ n == m,a(n), If[n == m - 1 || n == m + 1, If[n == m - 1, c(m - 1), If[n == m + 1, b(n - 1), 0]], 0]];

Example

{1},
{1, -1},
{-1, -2, 1},
{-3, 1, 3, -1},
{-1, 8, 0, -4, 1},
{5, 7, -14, -2, 5, -1},
{7, -14, -21, 20, 5, -6, 1},
{-3, -35, 21, 45, -25, -9, 7, -1},
{-17, -4, 98, -16, -80, 28, 14, -8, 1},
{-11, 83, 60, -204, -14,126, -28, -20, 9, -1},
{23, 102, -219, -232, 350, 84, -182, 24, 27, -10, 1}

Mathematica

a[n_] := 1; b[n_] := 2; c[n_] = 1; T[n_, m_, d_] := If[ n == m, a[n], If[n == m - 1 || n == m + 1, If[n == m - 1, c[m - 1], If[n == m + 1, b[n - 1], 0]], 0]]; MO[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; a0 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[MO[n], x], x], {n, 1, 10}]]; Flatten[a0]

Crossrefs

Sequence in context: A015710 A108415 A278572 * A111963 A206923 A328570

Adjacent sequences: A136641 A136642 A136643 * A136645 A136646 A136647

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Mar 31 2008

Status

approved