

A235089


a(n)*Pi is the total length of irregular spiral (center points: 2, 1, 3, 4) after n rotations.


6



3, 10, 13, 20, 23, 30, 33, 40, 43, 50, 53, 60, 63, 70, 73, 80, 83, 90, 93, 100, 103, 110, 113, 120, 123, 130, 133, 140, 143, 150, 153, 160, 163, 170, 173, 180, 183, 190, 193, 200, 203, 210, 213, 220, 223, 230, 233, 240, 243, 250, 253, 260, 263, 270, 273, 280, 283, 290, 293, 300, 303, 310, 313, 320, 323, 330, 333
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OFFSET

1,1


COMMENTS

Let points 2, 1, 3 & 4 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 point 3, 4, 1, ... and so on. The form is nonexpanded loop.
The alternative point order [2, 3, 1, 4] gives the same pattern with reflection, but the sequence will be 2*A047215(n). See illustration in links.
Conjecture: Numbers equivalent 0 or 3 modulo 10.  Ralf Stephan, Jan 13 2014


LINKS

Table of n, a(n) for n=1..67.
Kival Ngaokrajang, Illustration of initial terms


FORMULA

Conjecture: a(n) = 1+(1)^n+5*n. a(n) = a(n1)+a(n2)a(n3). G.f.: x*(7*x+3) / ((x1)^2*(x+1)).  Colin Barker, Jan 16 2014


PROG

(Small Basic)
a[1]=3
For n = 1 To 100
d1=3
If Math.Remainder(n+1, 2)=0 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). A234902*Pi, A234903*Pi, A234904*Pi (total spiral length, 3 inline center points).
Conjectured partial sums of A010705.
Sequence in context: A298418 A229205 A229483 * A022122 A042479 A042897
Adjacent sequences: A235086 A235087 A235088 * A235090 A235091 A235092


KEYWORD

nonn


AUTHOR

Kival Ngaokrajang, Jan 03 2014


STATUS

approved



