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 A235088 a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4) after n rotations. 6
 3, 6, 17, 28, 47, 66, 93, 120, 155, 190, 233, 276, 327, 378, 437, 496, 563, 630, 705, 780, 863, 946, 1037, 1128, 1227, 1326, 1433, 1540, 1655, 1770, 1893, 2016, 2147, 2278, 2417, 2556, 2703, 2850, 3005, 3160, 3323, 3486, 3657, 3828, 4007, 4186, 4373, 4560, 4755, 4950, 5153, 5356, 5567, 5778, 5997, 6216, 6443, 6670, 6905, 7140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let points 1, 2, 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 expanded spiral. See illustration in links. LINKS Kival Ngaokrajang, Illustration of initial terms FORMULA a(n) = 2*floor((n-1)^2/4) + 3*ceiling(n^2/2) (conjectured). - Ralf Stephan, Jan 13 2014 Conjecture: a(n) = 1-(-1)^n-n+2*n^2. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: -x*(5*x^2+3)/((x-1)^3*(x+1)). - Colin Barker, Jan 16 2014 PROG (Small Basic) a[1]=3 d1=3 For n = 1 To 100 If Math.Remainder(n+3, 2)=1 then d1=d1+8 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). Sequence in context: A217084 A024823 A024315 * A327068 A307604 A049943 Adjacent sequences: A235085 A235086 A235087 * A235089 A235090 A235091 KEYWORD nonn AUTHOR Kival Ngaokrajang, Jan 03 2014 STATUS approved

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Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)