A047607 -id:A047607 - cp's OEIS frontend

A236326 a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 1) after n rotations.

3, 6, 10, 17, 24, 27, 30, 34, 41, 48, 51, 54, 58, 65, 72, 75, 78, 82, 89, 96, 99, 102, 106, 113, 120, 123, 126, 130, 137, 144, 147, 150, 154, 161, 168, 171, 174, 178, 185, 192, 195, 198, 202, 209, 216, 219, 222, 226, 233, 240, 243, 246, 250, 257, 264, 267, 270, 274, 281, 288, 291, 294, 298, 305, 312, 315, 318, 322

Offset: 1

Kival Ngaokrajang, Jan 22 2014

nonn

Let points 1, 2, 3, 4, and 5 be placed on a horizontal straight line at intervals of 1 unit. (See illustration under Links.) Construct a continuous curve from half circles, alternately lying below and above the line, centered at points 1, 2, 3, 4, 5, 1, ... and so on, with the first half circle (centered at point 1) beginning at point 2.
Also floor(a(n)/3) = A047607(n+1).
Conjecture: All forms of 120 permutations of 5 center points are non-expanded loops.

Kival Ngaokrajang, Illustration of irregular spirals (center points: 1, 2, 3, 4, 5) Pattern 1.

Cf. A014105 (2 center points); A234902, A234903, A234904 (3 center points); A235088, A235089 (4 center points).

Conjecture from Colin Barker, Jul 12 2014: (Start)
a(n) = a(n-1)+a(n-5)-a(n-6).
G.f.: x*(7*x^4+7*x^3+4*x^2+3*x+3) / ((x-1)^2*(x^4+x^3+x^2+x+1)). (End)

Description of procedure for constructing curve (under Comments) edited by Jon E. Schoenfield, Feb 12 2014

cp's OEIS Frontend

A236326 a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 1) after n rotations.

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