A122773 Triangular array, see Mathematica code.

2, 1, -1, -4, 2, 1, 4, -4, 2, -1, -16, 24, -16, 4, 1, 16, -32, 28, -12, 3, -1, -64, 160, -176, 104, -36, 6, 1, 64, -192, 256, -192, 88, -24, 4, -1, -256, 896, -1408, 1280, -736, 272, -64, 8, 1, 256, -1024, 1856, -1984, 1376, -640, 200, -40, 5, -1, -1024, 4608, -9472, 11648, -9472, 5312, -2080, 560, -100, 10, 1, 1024

Offset: 1

Author

Gary W. Adamson and Roger L. Bagula, Oct 20 2006

Keywords

• uned
• tabl
• sign
• obsc
• less

Examples

			Triangular array:
  {2},
  {1, -1},
  {-4, 2, 1},
  {4, -4, 2, -1},
  {-16, 24, -16, 4, 1},
  {16, -32, 28, -12, 3, -1},
  {-64, 160, -176, 104, -36, 6, 1},
  {64, -192, 256, -192, 88, -24, 4, -1}
		

References

• Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.

Links

• J. Kappraff, D. Blackmore, and G. Adamson, Phyllotaxis as a Dynamical System: A Study in Number, In Symmetry in Plants edited by R.V. Jean and D. Barabe. Singapore: World Scientific. (1996).

Programs

Mathematica

An[d_] := Table[If[n == d, 1, If[m == n + 1, 1, 0]], {n, 1, d}, {m, 1, d}];
Join[{{2}}, Table[CoefficientList[CharacteristicPolynomial[2*IdentityMatrix[d] + MatrixPower[An[d], -1], x], x], {d, 1, 20}]]
Flatten[%]