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

Author

Robert G. Wilson v, May 31 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Inspired by the first difference of A108752.

Programs

Mathematica

PadRight[{}, 105, {1, 3, 5, 3}]
CoefficientList[Series[(3 x^2 + 2 x + 1)/(-x^3 + x^2 - x + 1), {x, 0, 104}], x]
LinearRecurrence[{1, -1, 1}, {1, 3, 5}, 105]
RecurrenceTable[{a[n] == a[n - 1] - a[n - 2] + a[n - 3], a[1] == 1, a[2] == 3, a[3] == 5}, a, {n, 105}]
Table[{1, 3, 5, 3}, 10] // Flatten (* Eric W. Weisstein, Feb 07 2025 *)
Table[3 - 2 Sin[n Pi/2], {n, 20}] (* Eric W. Weisstein, Feb 07 2025 *)
3 - 2 Sin[Range[20] Pi/2] (* Eric W. Weisstein, Feb 07 2025 *)

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