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

1,1

Links

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

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.

Cf. A029744, A048673, A246360.

Sequence in context: A345984 A191198 A191137 * A069061 A088811 A007977

Adjacent sequences: A247281 A247282 A247283 * A247285 A247286 A247287

Keyword

nonn

Author

Antti Karttunen, Sep 11 2014

Status

approved