|
%I #22 Jan 01 2023 13:47:29
%S 2,1,-1,-4,2,1,4,-4,2,-1,-16,24,-16,4,1,16,-32,28,-12,3,-1,-64,160,
%T -176,104,-36,6,1,64,-192,256,-192,88,-24,4,-1,-256,896,-1408,1280,
%U -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
%N Triangular array, see Mathematica code.
%D Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
%H J. Kappraff, D. Blackmore, and G. Adamson, <a href="https://doi.org/10.1142/9789814261074_0017">Phyllotaxis as a Dynamical System: A Study in Number</a>, In Symmetry in Plants edited by R.V. Jean and D. Barabe. Singapore: World Scientific. (1996).
%e Triangular array:
%e {2},
%e {1, -1},
%e {-4, 2, 1},
%e {4, -4, 2, -1},
%e {-16, 24, -16, 4, 1},
%e {16, -32, 28, -12, 3, -1},
%e {-64, 160, -176, 104, -36, 6, 1},
%e {64, -192, 256, -192, 88, -24, 4, -1}
%t An[d_] := Table[If[n == d, 1, If[m == n + 1, 1, 0]], {n, 1, d}, {m, 1, d}];
%t Join[{{2}}, Table[CoefficientList[CharacteristicPolynomial[2*IdentityMatrix[d] + MatrixPower[An[d], -1], x], x], {d, 1, 20}]]
%t Flatten[%]
%K uned,tabl,sign,obsc,less
%O 1,1
%A _Gary W. Adamson_ and _Roger L. Bagula_, Oct 20 2006
|
