This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A236326 a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 1) after n rotations. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Kival Ngaokrajang, Illustration of irregular spirals (center points: 1, 2, 3, 4, 5) Pattern 1. FORMULA 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) PROG (Small Basic) n =5       'center points number 1<=n<=9 pt=-1      'pattern1: pt=-1; pattern2: pt=1 i=12345    'center points order rota=100   'rotations sum=0 rc=1 r[1]=1 For i1 = 1 To n   d1=i/Math.Power(10, 1)   i=math.Floor(d1)   d[i1]=(d1-i)*Math.Power(10, 1) EndFor For j1=1 To n   For j2=1 To n     If d[j1]=j2 Then       dd[j2]=j1     endif   EndFor EndFor For j3=1 To n   If j3=n Then     dxy[j3]=dd[j3]-dd[1]   Else     dxy[j3]=dd[j3]-dd[j3+1]   EndIf EndFor For k1=1 To rota*n   cc=Math.Floor((k1-1)/n)   p[k1]=r[k1]+pt*dxy[k1-cc*n]*Math.Power(-1, Math.Remainder(k1, 2))   r[k1+1]=p[k1]   sum=sum+math.Abs(r[k1])   If math.Abs(r[k1])>0 Then     rc=rc+1   EndIf   If rc=3 Then     TextWindow.Write(sum+", ")     rc=1   EndIf EndFor CROSSREFS Cf. A014105 (2 center points); A234902, A234903, A234904 (3 center points); A235088, A235089 (4 center points). Sequence in context: A318290 A291986 A094272 * A308699 A286304 A005045 Adjacent sequences:  A236323 A236324 A236325 * A236327 A236328 A236329 KEYWORD nonn AUTHOR Kival Ngaokrajang, Jan 22 2014 EXTENSIONS Description of procedure for constructing curve (under Comments) edited by Jon E. Schoenfield, Feb 12 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 07:30 EDT 2019. Contains 328051 sequences. (Running on oeis4.)