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A247284 Subrecords in A048673: maximum value between two consecutive records in A048673.

%I A247284 #15 Jan 14 2025 14:58:26
%S A247284 4,6,13,18,38,63,113,188,338,563,1013,1688,3038,5063,9113,15188,27338,
%T A247284 45563,82013,136688,246038,410063,738113,1230188,2214338,3690563,
%U A247284 6643013,11071688,19929038,33215063,59787113,99645188,179361338,298935563,538084013,896806688
%N A247284 Subrecords in A048673: maximum value between two consecutive records in A048673.
%H A247284 Antti Karttunen, <a href="/A247284/b247284.txt">Table of n, a(n) for n = 1..60</a>
%F A247284 a(n) = A048673(A247283(n)).
%F A247284 Conjectures from _Chai Wah Wu_, Jul 30 2020: (Start)
%F A247284 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n > 7.
%F A247284 G.f.: x*(-10*x^6 + 10*x^5 - x^4 - x^3 - 5*x^2 + 2*x + 4)/((x - 1)*(3*x^2 - 1)). (End)
%e A247284 The fourth (A246360(4) = 5) and the fifth (A246360(5) = 8) record of A048673 (1, 2, 3, 5, 4, 8, ...) occur at A029744(4) = 4 and A029744(5) = 6 respectively. In range between, the maximum must occur at 5, where A048673(5) = 4, thus a(4-3) = a(1) = 4. (All the previous records of A048673 are in consecutive positions, 1, 2, 3, 4, thus there are no previous subrecords).
%e A247284 The ninth (A246360(9) = 68) and the tenth (A246360(10) = 122) record of A048673 occur at A029744(9) = 24 and A029744(10) = 32 respectively. For n in range 25 .. 31 the values of A048673 are: 25, 26, 63, 50, 16, 53, 19, of which 63 is the maximum, thus a(9-3) = a(6) = 63.
%o A247284 (PARI) \\ See program in A247283.
%o A247284 (Scheme) (define (A247284 n) (A048673 (A247283 n)))
%Y A247284 A247283 gives the corresponding positions.
%Y A247284 Cf. A029744, A048673, A246360.
%K A247284 nonn
%O A247284 1,1
%A A247284 _Antti Karttunen_, Sep 11 2014