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%I #46 Oct 04 2023 10:38:58
%S 1,6,20,120,272,1632,5440,32640,65792,394752,1315840,7895040,17895424,
%T 107372544,357908480,2147450880,4295032832,25770196992,85900656640,
%U 515403939840,1168248930304,7009493581824,23364978606080
%N Decimal number generated by the binary bits of the n-th generation of the Rule 102 elementary cellular automaton.
%C Central diagonal of A099884 when viewed as a square array. Thus also a subsequence of A118666. - _Antti Karttunen_, Jan 18 2020
%H Robert Price, <a href="/A117998/b117998.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule102.html">Rule 102</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F It appears that a(n) = A099885(2*n). - _Peter Bala_, Feb 01 2017
%F From _Antti Karttunen_, Jan 19 2020: (Start)
%F Bala's observation is correct, and follows from the formula given below and from the fact that this is the central diagonal of square array A099884.
%F a(n) = A000079(n) * A001317(n). [See Eric Weisstein's World of Mathematics -link]
%F a(0) = 1; for n > 0, a(n) = A048726(a(n-1)).
%F (End)
%e 1; 1, 1, 0; 1, 0, 1, 0, 0; 1, 1, 1, 1, 0, 0, 0; 1, 0, 0, 0, 1, 0, 0, 0, 0; ...
%t NestList[BitXor[4#,2#]&,1,50] (* _Paolo Xausa_, Oct 04 2023 *)
%o (PARI) A117998(n) = (subst(lift(Mod(1+'x, 2)^n), 'x, 2)<<n); \\ _Antti Karttunen_, Jan 19 2020, after _Gheorghe Coserea_'s code for A001317.
%o (Python)
%o def A117998(n): return sum((bool(~n&n-k)^1)<<k for k in range(n+1))<<n # _Chai Wah Wu_, May 03 2023
%Y Iterates of A048726, starting from a(0) = 1.
%Y Central diagonal of A099884. Bisection of A099885. Subsequence of A118666.
%Y Cf. A000079, A001317, A193231.
%K nonn,base
%O 0,2
%A _Eric W. Weisstein_, Apr 08 2006
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