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Table read by rows: row n is the n-th Primary Phyllotaxis Sequence (PPS), which has F(n+1) terms, where F(n) is the n-th Fibonacci number. For 1 <= k < F(n+1), a(n, k) = -k*F(n-1) mod F(n+1). a(n, F(n+1)) = F(n+1).
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%I #12 Apr 25 2018 03:28:07

%S 1,1,2,2,1,3,3,1,4,2,5,5,2,7,4,1,6,3,8,8,3,11,6,1,9,4,12,7,2,10,5,13,

%T 13,5,18,10,2,15,7,20,12,4,17,9,1,14,6,19,11,3,16,8,21,21,8,29,16,3,

%U 24,11,32,19,6,27,14,1,22,9,30,17,4,25,12,33,20,7,28,15,2,23,10,31,18,5,26

%N Table read by rows: row n is the n-th Primary Phyllotaxis Sequence (PPS), which has F(n+1) terms, where F(n) is the n-th Fibonacci number. For 1 <= k < F(n+1), a(n, k) = -k*F(n-1) mod F(n+1). a(n, F(n+1)) = F(n+1).

%C Related to the arrangement of stalks or florets on a plant.

%C In the reference, the rows of the table appear as rings of the Primary Phyllotaxis Wheel, alternating clockwise and counterclockwise.

%D Jay Kappraff, "Beyond Measure, A Guided Tour Through Nature, Myth and Number", World Scientific, 2002, p. 522-538., (p. 535, Adamson's Primary Phyllotaxis Wheel).

%H Jay Kappraff, <a href="http://www.scipress.org/journals/forma/pdf/1904/19040335.pdf">Growth in Plants: A Study in Number</a>

%e The row of 13 terms starts with 8. Successive terms are obtained by subtracting 5 or adding 8: 8, 3, 11, 6, 1, 9, 4, 12, 7, 2, 10, 5, 13.

%K nonn,easy,tabf

%O 1,3

%A _Gary W. Adamson_, Apr 04 2004

%E Edited by _David Wasserman_, Oct 26 2006