login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..60.

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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)