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A136643
Triangle of coefficients of characteristic polynomials of anti-symmetrical tridiagonal matrices: Middle diagonal: a=1; Lower first subdiagonal: b=2; Upper first subdiagonal: c=-2; Example: M(3) {{1, -2, 0}, {2, 1, -2}, {0, 2, 1}}.
0
1, 1, -1, 5, -2, 1, 9, -11, 3, -1, 29, -28, 18, -4, 1, 65, -101, 58, -26, 5, -1, 181, -278, 231, -100, 35, -6, 1, 441, -863, 741, -435, 155, -45, 7, -1, 1165, -2416, 2528, -1576, 730, -224, 56, -8, 1, 2929, -7033, 7908, -5844, 2926, -1134, 308, -68, 9, -1, 7589, -19626, 25053, -20056, 11690, -4956, 1666, -408, 81, -10, 1
OFFSET
1,4
COMMENTS
Row sums are:
{1, 0, 4, 0, 16, 0, 64, 0, 256, 0, 1024}
REFERENCES
Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 516.
FORMULA
a(n)= 1; b(n)= 2; c(n) = -2; 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},
{5, -2, 1},
{9, -11, 3, -1},
{29, -28, 18, -4, 1},
{65, -101, 58, -26, 5, -1},
{181, -278, 231, -100, 35, -6, 1},
{441, -863, 741, -435, 155, -45,7, -1},
{1165, -2416, 2528, -1576, 730, -224, 56, -8, 1},
{2929, -7033, 7908, -5844, 2926, -1134, 308, -68,9, -1},
{7589, -19626, 25053, -20056, 11690, -4956, 1666, -408, 81, -10, 1}
MATHEMATICA
a[n_] := 1; b[n_] := 2; c[n_] = -2; 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: A318328 A371848 A011507 * A118438 A336244 A083801
KEYWORD
uned,tabl,sign
AUTHOR
Roger L. Bagula, Mar 31 2008
STATUS
approved