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

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

Author

Antti Karttunen, Sep 11 2014

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..60

Crossrefs

A247283 gives the corresponding positions.

Cf. A029744, A048673, A246360.

Programs

PARI

\\ See program in A247283.

Scheme

(define (A247284 n) (A048673 (A247283 n)))

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)