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A246360 a(1) = 1, then A007051 ((3^n)+1)/2 interleaved with A057198 (5*3^(n-1)+1)/2.

%I A246360 #35 Sep 02 2025 18:15:50
%S A246360 1,2,3,5,8,14,23,41,68,122,203,365,608,1094,1823,3281,5468,9842,16403,
%T A246360 29525,49208,88574,147623,265721,442868,797162,1328603,2391485,
%U A246360 3985808,7174454,11957423,21523361,35872268,64570082,107616803,193710245,322850408,581130734
%N A246360 a(1) = 1, then A007051 ((3^n)+1)/2 interleaved with A057198 (5*3^(n-1)+1)/2.
%C A246360 Also record values in A048673.
%H A246360 Antti Karttunen, <a href="/A246360/b246360.txt">Table of n, a(n) for n = 1..64</a>
%H A246360 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3).
%F A246360 a(1) = 1, a(2n) = (3^n+1)/2, a(2n+1) = (5 * 3^(n-1)+1)/2.
%F A246360 a(n) = A048673(A029744(n)).
%F A246360 a(n) = A087503(n-3) + 2 for n >= 3. - _Peter Kagey_, Nov 30 2019
%F A246360 G.f.: x -x^2*(-2-x+4*x^2) / ( (x-1)*(3*x^2-1) ). - _R. J. Mathar_, Sep 23 2014
%t A246360 LinearRecurrence[{1, 3, -3}, {1, 2, 3, 5}, 40] (* _Hugo Pfoertner_, Sep 27 2022 *)
%o A246360 (Scheme)
%o A246360 (define (A246360 n) (cond ((<= n 1) n) ((even? n) (/ (+ 1 (A000244 (/ n 2))) 2)) (else (/ (+ 1 (* 5 (A000244 (/ (- n 3) 2)))) 2))))
%o A246360 (Python)
%o A246360 def A246360(n): return 1 if n==1 else (3+((n&1)<<1))*3**((n>>1)-1)+1>>1 # _Chai Wah Wu_, Sep 02 2025
%Y A246360 Even bisection: A007051 from A007051(1) onward: [2, 5, 14, 41, ...]
%Y A246360 Odd bisection: 1 followed by A057198.
%Y A246360 A029744 gives the corresponding record positions in A048673.
%Y A246360 A247284 gives the maximum values of A048673 between these records and A247283 gives the positions where they occur.
%Y A246360 Subsequence of A246361.
%Y A246360 Cf. A000244, A193652, A246347.
%K A246360 nonn,easy,changed
%O A246360 1,2
%A A246360 _Antti Karttunen_, Aug 24 2014