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.

A000117 Number of even sequences with period 2n (bisection of A000011).

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%I A000117 M1150 N0438 #33 Jun 26 2022 04:14:55
%S A000117 1,2,4,8,18,44,122,362,1162,3914,13648,48734,176906,649532,2405236,
%T A000117 8964800,33588234,126390032,477353376,1808676326,6872485104,
%U A000117 26179922024,99957747388,382443112538,1466024067850,5629516646996,21651955485304,83400061453514
%N A000117 Number of even sequences with period 2n (bisection of A000011).
%D A000117 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000117 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000117 Alois P. Heinz, <a href="/A000117/b000117.txt">Table of n, a(n) for n = 0..500</a>
%H A000117 E. N. Gilbert and J. Riordan, <a href="http://projecteuclid.org/euclid.ijm/1255631587">Symmetry types of periodic sequences</a>, Illinois J. Math., 5 (1961), 657-665.
%F A000117 a(n) ~ 4^(n-1) / (2*n). - _Cedric Lorand_, Apr 18 2022
%t A000117 b[0] = 1; b[n_] := (2^Floor[n/2] + (Table[EulerPhi[2d]*2^(n/d)/(2n), {d, Divisors[n]}] // Accumulate // Last))/2; a[n_] := b[2n]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 07 2014 *)
%Y A000117 Cf. A000011.
%K A000117 nonn,easy,nice
%O A000117 0,2
%A A000117 _N. J. A. Sloane_
%E A000117 More terms from _David W. Wilson_, Jan 13 2000