

A234902


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


8



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
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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 nonexpanded 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



FORMULA

G.f.: x*(7*x^4 + 4*x^3 + 4*x^2 + 7*x + 2)/((1x)*(1x^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).


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



