A287765 Period 4: repeat [1, 3, 5, 3].

1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1

Offset

1,2

Links

Table of n, a(n) for n=1..105.

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

Formula

G.f.: x * (3*x^2+2*x+1) / (1-x+x^2-x^3). [Corrected by Georg Fischer, May 19 2019]

a(n) = a(n-1) - a(n-2) + a(n-3) with a(1)=1, a(2)=3 and a(3)=5.

a(2n) = 3, a(4*n+1) = 1 and a(4*n+3) = 5.

a(n) = ((n+3) mod 4) + ((n+4) mod 4). - Aaron J Grech, Aug 30 2024

Mathematica

PadRight[{}, 105, {1, 3, 5, 3}] (* or *)
f[n_] := Switch[Mod[n, 4], 0, 3, 1, 1, 2, 3, 3, 5]; Array[f, 105] (* or *)
CoefficientList[ Series[(3x^2 +2x +1)/(-x^3 +x^2 -x +1), {x, 0, 104}], x] (* or *)
LinearRecurrence[{1, -1, 1}, {1, 3, 5}, 105] (* or *)
RecurrenceTable[{a[n] == a[n - 1] - a[n - 2] + a[n - 3], a[1] == 1, a[2] == 3, a[3] == 5}, a, {n, 105}]

Crossrefs

Inspired by the first difference of A108752.

Sequence in context: A103728 A243533 A239730 * A162777 A241014 A173454

Adjacent sequences: A287762 A287763 A287764 * A287766 A287767 A287768

Keyword

nonn,easy

Author

Robert G. Wilson v, May 31 2017

Status

approved