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A131093 a(1)=1, a(n) = a(n-1) + sum of odd numbers which are among the first (n-1) terms of the sequence.

%I A131093 #10 Feb 16 2025 08:33:06
%S A131093 1,2,3,7,18,29,69,178,287,683,1762,2841,6761,17442,28123,66927,172658,
%T A131093 278389,662509,1709138,2755767,6558163,16918722,27279281,64919121,
%U A131093 167478082,270037043,642633047,1657862098,2673091149
%N A131093 a(1)=1, a(n) = a(n-1) + sum of odd numbers which are among the first (n-1) terms of the sequence.
%C A131093 a(n) mod 2 = A011655(n+1);
%C A131093 a(n) = a(n-1) + Sum(a(k)*(a(k) mod 2): 1<=k<n), a(1) = 1.
%H A131093 Harvey P. Dale, <a href="/A131093/b131093.txt">Table of n, a(n) for n = 1..1000</a>
%H A131093 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddNumber.html">Odd Number</a>
%F A131093 Empirical g.f.: -x*(x-1)*(x^4+3*x^3+6*x^2+3*x+1) / (x^6-10*x^3+1). - _Colin Barker_, Mar 29 2013
%t A131093 nxt[{ot_,a_}]:=Module[{x=a+ot},{If[OddQ[x],ot+x,ot],x}]; NestList[nxt,{1,1},30][[All,2]] (* _Harvey P. Dale_, Dec 18 2020 *)
%Y A131093 Cf. A096777, A101135.
%K A131093 nonn
%O A131093 1,2
%A A131093 _Reinhard Zumkeller_, Jun 14 2007