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A247284
Subrecords in A048673: maximum value between two consecutive records in A048673.
4
4, 6, 13, 18, 38, 63, 113, 188, 338, 563, 1013, 1688, 3038, 5063, 9113, 15188, 27338, 45563, 82013, 136688, 246038, 410063, 738113, 1230188, 2214338, 3690563, 6643013, 11071688, 19929038, 33215063, 59787113, 99645188, 179361338, 298935563, 538084013, 896806688
OFFSET
1,1
LINKS
FORMULA
a(n) = A048673(A247283(n)).
Conjectures from Chai Wah Wu, Jul 30 2020: (Start)
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n > 7.
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)
EXAMPLE
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).
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.
PROG
(PARI): See program in A247283.
(Scheme) (define (A247284 n) (A048673 (A247283 n)))
CROSSREFS
A247283 gives the corresponding positions.
Sequence in context: A345984 A191198 A191137 * A069061 A373945 A088811
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 11 2014
STATUS
approved