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A217831 Triangle read by rows: label the entries T(0,0), T(1,0), T(0,1), T(2,0), T(1,1), T(0,2), T(3,0), ... Then T(n,k)=T(k,n), T(0,0)=0, T(1,0)=1, and for n>1, T(n,0)=0 and T(n,in+j)=T(n-j,j) (i,j >= 0, not both 0). 0
0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

Turner defined his triangle T by use of a 'neck-tie' device, and a 'double-cycling' procedure, in order to define his cycle-numbers. See the links below for further details.

LINKS

Table of n, a(n) for n=0..95.

John C. Turner, Musings of a Mathematician

John C. Turner, William J. Rogers, A representation of the natural numbers by means of cycle-numbers, with consequences in number theory, Annales Mathematicae et Informaticae, 41 (2013) pp. 235-254. Presented to the Fifteenth International Conference on Fibonacci numbers and Their Applications, in Eger, Hungary, on 25 June 2012. See also.

EXAMPLE

Triangle begins:

[0],

[1, 1],

[0, 1, 0],

[0, 1, 1, 0],

[0, 1, 0, 1, 0],

[0, 1, 1, 1, 1, 0],

[0, 1, 0, 0, 0, 1, 0],

[0, 1, 1, 1, 1, 1, 1, 0],

[0, 1, 0, 1, 0, 1, 0, 1, 0],

[0, 1, 1, 0, 1, 1, 0, 1, 1, 0],

[0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0],

[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],

...

MAPLE

T:=proc(n, k) option remember; local i, j;

if n=0 and k=0 then 0;

elif n=1 then 1;

elif k=0 or k=n then 0;

elif k>n then T(k, n);

else j:= (k mod n); i:=(k-j)/n; T(n-j, j); fi; end;

g:=n->[seq(T(n-i, i), i=0..n)];

[seq(g(n), n=0..20)];

MATHEMATICA

T[n_, k_] := T[n, k] = Module[{i, j}, Which[n == 0 && k == 0, 0, n == 1, 1, k == 0 || k == n, 0, k>n, T[k, n], True, j = Mod[k, n]; i = (k-j)/n; T[n-j, j]]]; g[n_] := Table[T[n-i, i], {i, 0, n}]; Table[g[n], {n, 0, 20}] // Flatten (* Jean-Fran├žois Alcover, Mar 06 2014, after Maple *)

CROSSREFS

Sequence in context: A286493 A189084 A286490 * A284848 A286484 A286487

Adjacent sequences:  A217828 A217829 A217830 * A217832 A217833 A217834

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 14 2012

STATUS

approved

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Last modified November 20 13:59 EST 2017. Contains 294972 sequences.