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%I #7 Mar 30 2012 18:57:43
%S 1,0,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,1,1,1,
%T 1,1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,1,1,1,0,1,1,1,1,0,1,1,0,
%U 1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,1
%N Triangular array: T(n,k)=[<n*r>+<k*r>], where [ ] = floor, < > = fractional part, and r = (1+sqrt(5))/2 (the golden ratio).
%C n-th row sum gives the number of k in [0,n] for which <n*r>+<k*r> > 1; see A194662.
%C Triangles of this sort and their row sums are sampled by the following sequences:
%C A194661-A194662: r=(1+sqrt(5))/2
%C A194663-A194665: r=sqrt(2)
%C A194666-A194668: r=sqrt(3)
%C A194669-A194671: r=sqrt(5)
%C A194675-A194678: r=e
%C A194679-A194682: r=3-sqrt(2)
%C A194683-A194686: r=(1+sqrt(3))/2
%e First 13 rows:
%e 1
%e 0 0
%e 1 1 1
%e 1 0 1 0
%e 0 0 0 0 0
%e 1 0 1 1 0 1
%e 0 0 1 0 0 1 0
%e 1 1 1 1 1 1 1 1
%e 1 0 1 1 0 1 0 1 1
%e 0 0 1 0 0 0 0 1 0 0
%e 1 1 1 1 0 1 1 1 1 0 1
%e 1 0 1 0 0 1 0 1 0 0 1 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 0
%t r = GoldenRatio; z = 14;
%t p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t h[n_, k_] := f[p[n*r] + p[k*r]]
%t Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t (* A194661 *)
%t TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t t[n_] := Sum[h[n, k], {k, 1, n}]
%t Table[t[n], {n, 1, 100}] (* A194662 *)
%Y Cf. A194662.
%K nonn,tabl
%O 1
%A _Clark Kimberling_, Sep 01 2011
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