A306764 a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].

1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6

Offset

0,3

Comments

a(1) to a(12) is a palindrome.

A089145(n) = A089128(n+3).

A089128(n) = A089145(n+3).

a(1) + a(2) + a(3) + a(4) = a(5) + a(6) + a(7) + a(8) = a(9) + a(10) + a(11) + a(12) = 10.

Links

Table of n, a(n) for n=0..71.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,-1,0,0,1).

Formula

a(n) = 2*A064038(n+3)/A306368(n).

a(n) = interleave A089128(n-1), A089128(n+1).

a(n) = interleave A089145(n+2), A089145(n-2).

From Colin Barker, Dec 09 2019: (Start)

G.f.: (1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)).

a(n) = a(n-3) - a(n-6) + a(n-9) for n>8.

(End)

Example

a(0) =  6/6  = 1;
a(1) = 10/10 = 1;
a(2) = 30/5  = 6;
a(3) = 42/21 = 2.

Mathematica

PadRight[{}, 120, {1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6}] (* or *) LinearRecurrence[ {0, 0, 1, 0, 0, -1, 0, 0, 1}, {1, 1, 6, 2, 1, 3, 2, 2, 3}, 120] (* Harvey P. Dale, Dec 16 2021 *)

Prog

(PARI) Vec((1 + x + 6*x^2 + x^3 - 3*x^5 + x^6 + 2*x^7 + 6*x^8) / ((1 - x)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)) + O(x^80)) \\ Colin Barker, Dec 11 2019

Crossrefs

Cf. A064038, A089128 and A089145 (shifted bisections), A306368, A010692.

Sequence in context: A284761 A021165 A165061 * A101607 A039508 A324569

Adjacent sequences: A306761 A306762 A306763 * A306765 A306766 A306767

Keyword

nonn,easy

Author

Paul Curtz, Mar 08 2019

Status

approved