A109008 -id:A109008 - cp's OEIS frontend

A302773 Numerators of (3*n + 2)/12.

1, 5, 2, 11, 7, 17, 5, 23, 13, 29, 8, 35, 19, 41, 11, 47, 25, 53, 14, 59, 31, 65, 17, 71, 37, 77, 20, 83, 43, 89, 23, 95, 49, 101, 26, 107, 55, 113, 29, 119, 61, 125, 32, 131, 67, 137, 35, 143, 73, 149, 38, 155, 79, 161, 41, 167, 85, 173, 44, 179, 91, 185, 47, 191, 97

Offset: 0

Bruno Berselli, Apr 13 2018

Or numerators of (3*n+2)/4. - Altug Alkan, Apr 17 2018

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Cf. A016789, A109008.
Cf. A060819: numerators of n/4, with n > 0.
Cf. A176672: numerators of (3*n + 1)/12.
First bisection is A165355; second bisection is A016969.

List([0..70], n -> NumeratorRat((3*n+2)/12));

Magma
```
[Numerator((3*n+2)/12): n in [0..70]];
```

Table[Numerator[(3 n + 2)/12], {n, 0, 70}]
LinearRecurrence[{0,0,0,2,0,0,0,-1},{1,5,2,11,7,17,5,23},80] (* Harvey P. Dale, Feb 04 2021 *)

vector(70, n, n--; numerator((3*n+2)/12))

Vec((1 + 5*x + 2*x^2 + 11*x^3 + 5*x^4 + 7*x^5 + x^6 + x^7)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2) + O(x^60)) \\ Colin Barker, Apr 16 2018

[numerator((3*n+2)/12) for n in (0..70)]

G.f.: (1 + 5*x + 2*x^2 + 11*x^3 + 5*x^4 + 7*x^5 + x^6 + x^7)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8).
a(n) = (3*n + 2)*(((-1)^n + 1)*(i^(n*(n+1)) - 5) + 16)/16, where i = sqrt(-1).
a(n) = A016789(n)/A109008(n+2).

A133186 Period 4: repeat [1, 2, 1, -4].

Original entry on oeis.org

1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4, 1, 2, 1, -4

Offset: 0

Paul Curtz, Oct 07 2007

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

Cf. A056594, A109008.

&cat [[1, 2, 1, -4]^^30]; // Wesley Ivan Hurt, Jul 09 2016

seq(op([1, 2, 1, -4]), n=0..40); # Wesley Ivan Hurt, Jul 09 2016

PadRight[{}, 100, {1, 2, 1, -4}] (* Wesley Ivan Hurt, Jul 09 2016 *)

G.f.: 1/(1+x)+3x/(1+x^2). a(n) = (-1)^n+3*A056594(n-1). [R. J. Mathar, Oct 30 2008]
From Wesley Ivan Hurt, Jul 09 2016: (Start)
a(n) + a(n-1) + a(n-2) + a(n-3) = 0 for n>2, a(n) = a(n-4) for n>3.
a(n) = cos(n*Pi) + 3*sin(n*Pi/2). (End)

cp's OEIS Frontend

A302773 Numerators of (3*n + 2)/12.

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