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A186347 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186346.

%I A186347 #16 Apr 11 2024 21:18:28
%S A186347 1,2,4,6,8,10,13,16,19,22,26,30,34,38,43,48,53,58,64,70,76,82,89,96,
%T A186347 103,110,118,126,134,142,151,160,169,178,188,198,208,218,229,240,251,
%U A186347 262,274,286,298,310,323,336,349,362,376,390,404,418,433,448,463,478,494,510,526,542,559,576,593,610,628,646,664,682,701,720,739,758,778,798,818,838,859,880,901,922,944,966,988,1010
%N A186347 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2.  Complement of A186346.
%C A186347 a(n) = a(-8-n) for all n in Z using the formula. - _Michael Somos_, Apr 05 2024
%H A186347 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F A186347 a(n)=n+floor(sqrt(8n-1/2))=A186346(n).
%F A186347 b(n)=n+floor((n^2+1/2)/8)=A186347(n).
%F A186347 G.f.: x*(1 + x^2 - x^4)/((1 - x)^2 * (1 - x^4)). - _Michael Somos_, Apr 05 2024
%e A186347 First, write
%e A186347 ....8....16..24..32..40..48..56..64..72..80.. (8i)
%e A186347 1..4..9..16...25...36......49....64.......81 (squares)
%e A186347 Then replace each number by its rank, where ties are settled by ranking 8i before the square:
%e A186347 a=(3,5,7,9,11,12,14,15,17,..)=A186346
%e A186347 b=(1,2,4,6,8,10,13,16,19,...)=A186347.
%t A186347 (* See A186346. *)
%o A186347 (PARI) a(n) = (n + 4)^2\8 - 2; \\ _Michael Somos_, Apr 05 2024
%o A186347 (PARI) a(n)=n^2\8 + n \\ _Charles R Greathouse IV_, Apr 11 2024
%Y A186347 Cf. A186346, A186348, A186349.
%K A186347 nonn,easy
%O A186347 1,2
%A A186347 _Clark Kimberling_, Feb 20 2011