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Search: id:A136643
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| A136643 |
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Triangle of coefficients of characteristic polynomials of anti-symmetrical tridiagonal matrices: Middle diagonal : a=1; Lower first sub-diagonal:b=2; Upper first sub-diagonal:c=-2; Example:M(3) {{1, -2, 0}, {2, 1, -2}, {0, 2, 1}}. |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{1, 0, 4, 0, 16, 0, 64, 0, 256, 0, 1024}
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REFERENCES
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Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 516.
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FORMULA
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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]];
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A111395 A011394 A011507 this_sequence A118438 A083801 A111544
Adjacent sequences: A136640 A136641 A136642 this_sequence A136644 A136645 A136646
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 31 2008
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