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

Author

Bruno Berselli, Apr 13 2018

Keywords

• nonn
• easy
• frac

Comments

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

Links

• 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).

Crossrefs

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.

Programs

GAP

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

Magma

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

Mathematica

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 *)

PARI

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

PARI

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

Sage

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

Formula

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).