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

1,2

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).

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

Mathematica

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

Prog

(Scheme)
(define (A246360 n) (cond ((<= n 1) n) ((even? n) (/ (+ 1 (A000244 (/ n 2))) 2)) (else (/ (+ 1 (* 5 (A000244 (/ (- n 3) 2)))) 2))))
(Python)
def A246360(n): return 1 if n==1 else (3+((n&1)<<1))*3**((n>>1)-1)+1>>1 # Chai Wah Wu, Sep 02 2025

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.

Sequence in context: A318520 A039828 A357303 * A005627 A191794 A191388

Adjacent sequences: A246357 A246358 A246359 * A246361 A246362 A246363

Keyword

nonn,easy

Author

Antti Karttunen, Aug 24 2014

Status

approved