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A373185 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 - 1 + A(x^4).

%I A373185 #18 May 27 2024 22:39:57
%S A373185 2,3,4,7,6,7,8,12,10,11,12,17,14,15,16,24,18,19,20,27,22,23,24,32,26,
%T A373185 27,28,37,30,31,32,45,34,35,36,47,38,39,40,52,42,43,44,57,46,47,48,66,
%U A373185 50,51,52,67,54,55,56,72,58,59,60,77,62,63,64,89,66,67,68,87,70,71,72,92,74,75,76,97,78,79,80,108,82,83,84,107
%N A373185 G.f. A(x) satisfies A(x) = 1/(1 - x)^2 - 1 + A(x^4).
%H A373185 Seiichi Manyama, <a href="/A373185/b373185.txt">Table of n, a(n) for n = 1..10000</a>
%F A373185 a(4*n+1) = 4*n+2, a(4*n+2) = 4*n+3, a(4*n+3) = 4*n+4 and a(4*n+4) = 4*n+5 + a(n+1) for n >= 0.
%F A373185 G.f.: A(x) = Sum_{k>=0} (1/(1 - x^(4^k))^2 - 1).
%o A373185 (Ruby)
%o A373185 def A(k, n)
%o A373185   ary = [0]
%o A373185   (1..n).each{|i|
%o A373185     j = i + 1
%o A373185     j += ary[i / k] if i % k == 0
%o A373185     ary << j
%o A373185   }
%o A373185   ary[1..-1]
%o A373185 end
%o A373185 p A(4, 90)
%Y A373185 Cf. A084432, A373184.
%K A373185 nonn,easy
%O A373185 1,1
%A A373185 _Seiichi Manyama_, May 27 2024