A234903 a(n)*Pi is the total length of irregular spiral (center points: 1, 3, 2) after n rotations.

4, 11, 13, 20, 24, 28, 35, 37, 44, 48, 52, 59, 61, 68, 72, 76, 83, 85, 92, 96, 100, 107, 109, 116, 120, 124, 131, 133, 140, 144, 148, 155, 157, 164, 168, 172, 179, 181, 188, 192, 196, 203, 205, 212, 216, 220, 227, 229, 236, 240, 244, 251, 253, 260, 264, 268, 275, 277, 284, 288, 292, 299, 301, 308, 312, 316, 323, 325

Offset

1,1

Comments

Let points 1, 3 & 2 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 spiral is a non-expanded loop. See illustration in links.

Links

Table of n, a(n) for n=1..68.

Kival Ngaokrajang, Illustration of initial terms

Formula

G.f.: x*(4*x^4 + 7*x^3 + 2*x^2 + 7*x + 4)/((1-x)(1-x^5)) (conjectured). - Ralf Stephan, Jan 13 2014

Prog

(Small Basic)
a[1]=4
For n = 1 To 100
  d1=2
  m5 = math.Remainder(n+1, 5)
  If m5 = 0 Or m5 = 1 Then
    d1 = 4
  EndIf
  If m5 = 2 Or m5 = 4 Then
    d1 = 7
  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: A066985 A228003 A347561 * A369615 A095797 A205846

Adjacent sequences: A234900 A234901 A234902 * A234904 A234905 A234906

Keyword

nonn

Author

Kival Ngaokrajang, Jan 01 2014

Status

approved