cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A194671 Number of k in [1,n] for which + > 1, where < > = fractional part and r = sqrt(5); row sums of A164670.

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%I A194671 #5 Mar 30 2012 18:57:43
%S A194671 0,0,2,4,1,2,5,8,2,4,7,11,1,4,8,13,0,4,8,14,20,4,9,16,23,4,10,17,25,2,
%T A194671 9,17,26,0,8,16,26,36,7,16,27,38,6,16,28,40,4,15,27,40,1,13,26,40,54,
%U A194671 12,25,40,55,10,24,40,56,7,22,38,55,3,19,36,54,72,17,34,53,72
%N A194671 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(5); row sums of A164670.
%t A194671 r = Sqrt[5]; z = 13;
%t A194671 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194671 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194671 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194671 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194671 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194669 *)
%t A194671 Table[s[n], {n, 1, 100}]
%t A194671 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194671 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194671   (* A194670 *)
%t A194671 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194671 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194671 Table[t[n], {n, 1, 100}]  (* A194671 *)
%Y A194671 Cf. A194670.
%K A194671 nonn
%O A194671 1,3
%A A194671 _Clark Kimberling_, Sep 01 2011