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

1, 2, 3, 5, 8, 14, 23, 41, 68, 122, 203, 365, 608, 1094, 1823, 3281, 5468, 9842, 16403, 29525, 49208, 88574, 147623, 265721, 442868, 797162, 1328603, 2391485, 3985808, 7174454, 11957423, 21523361, 35872268, 64570082, 107616803, 193710245, 322850408, 581130734

Offset: 1

Author

Antti Karttunen, Aug 24 2014

Keywords

• nonn
• easy

Comments

Also record values in A048673.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..64
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3).

Crossrefs

Even bisection: A007051 from A007051(1) onward: [2, 5, 14, 41, ...]

Odd bisection: 1 followed by A057198.

A029744 gives the corresponding record positions in A048673.

A247284 gives the maximum values of A048673 between these records and A247283 gives the positions where they occur.

Subsequence of A246361.

Cf. A000244, A193652, A246347.

Programs

Mathematica

LinearRecurrence[{1, 3, -3}, {1, 2, 3, 5}, 40] (* Hugo Pfoertner, Sep 27 2022 *)

Scheme

(define (A246360 n) (cond ((<= n 1) n) ((even? n) (/ (+ 1 (A000244 (/ n 2))) 2)) (else (/ (+ 1 (* 5 (A000244 (/ (- n 3) 2)))) 2))))

Formula

a(1) = 1, a(2n) = (3^n+1)/2, a(2n+1) = (5 * 3^(n-1)+1)/2.

a(n) = A048673(A029744(n)).

a(n) = A087503(n-3) + 2 for n >= 3. - Peter Kagey, Nov 30 2019

G.f.: x -x^2*(-2-x+4*x^2) / ( (x-1)*(3*x^2-1) ). - R. J. Mathar, Sep 23 2014