A234902 a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3) after n rotations.

2, 9, 13, 17, 24, 26, 33, 37, 41, 48, 50, 57, 61, 65, 72, 74, 81, 85, 89, 96, 98, 105, 109, 113, 120, 122, 129, 133, 137, 144, 146, 153, 157, 161, 168, 170, 177, 181, 185, 192, 194, 201, 205, 209, 216, 218, 225, 229, 233, 240, 242, 249, 253, 257

Offset

1,1

Comments

Let points 1, 2 & 3 be placed on a straight line at intervals of 1 unit. At point 1, make a half unit circle; then, at point 2, make another half circle and maintain continuity of circumferences. Continue using this procedure at points 3, 1, 2 and so on. The form of the spiral is a non-expanded loop.

The sequence will be A047622 if the second radius = 2; if the second radius = 0, the sequence is a(n).

See illustration in links.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Kival Ngaokrajang, Illustration of initial terms

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

Formula

G.f.: x*(7*x^4 + 4*x^3 + 4*x^2 + 7*x + 2)/((1-x)*(1-x^5)). - Ralf Stephan, Jan 20 2014

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {2, 9, 13, 17, 24, 26}, 60] (* Harvey P. Dale, May 21 2021 *)

Prog

(Small Basic)
a[1]=2
For n = 1 To 100
  d1=2
  m5=math.Remainder(n+1, 5)
  If m5=0 Or m5=2 Then
    d1=7
  EndIf
  If m5=3 Or m5=4 Then
    d1=4
  EndIf
  a[n+1]=a[n]+d1
  TextWindow.Write(a[n]+", ")
EndFor

Crossrefs

Cf. A014105*Pi (total spiral length, 2 inline center points).

Sequence in context: A287069 A068047 A044904 * A138946 A037385 A115907

Adjacent sequences: A234899 A234900 A234901 * A234903 A234904 A234905

Keyword

nonn,easy

Author

Kival Ngaokrajang, Jan 01 2014

Status

approved