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

%I A234903 #21 May 04 2021 01:09:34
%S A234903 4,11,13,20,24,28,35,37,44,48,52,59,61,68,72,76,83,85,92,96,100,107,
%T A234903 109,116,120,124,131,133,140,144,148,155,157,164,168,172,179,181,188,
%U A234903 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
%N A234903 a(n)*Pi is the total length of irregular spiral (center points: 1, 3, 2) after n rotations.
%C A234903 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.
%H A234903 Kival Ngaokrajang, <a href="/A234903/a234903.pdf">Illustration of initial terms</a>
%F A234903 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
%o A234903 (Small Basic)
%o A234903 a[1]=4
%o A234903 For n = 1 To 100
%o A234903   d1=2
%o A234903   m5 = math.Remainder(n+1,5)
%o A234903   If m5 = 0 Or m5 = 1 Then
%o A234903     d1 = 4
%o A234903   EndIf
%o A234903   If m5 = 2 Or m5 = 4 Then
%o A234903     d1 = 7
%o A234903   EndIf
%o A234903   a[n+1]=a[n]+d1
%o A234903   TextWindow.Write(a[n]+", ")
%o A234903 EndFor
%Y A234903 Cf. A014105*Pi (total spiral length, 2 inline center points).
%K A234903 nonn
%O A234903 1,1
%A A234903 _Kival Ngaokrajang_, Jan 01 2014