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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
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.
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 * A369707 A327068 A307604
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Jan 03 2014
STATUS
approved