The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A235088 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A235088

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

#19 by Hugo Pfoertner at Fri Oct 22 15:31:42 EDT 2021

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#18 by Amiram Eldar at Fri Oct 22 15:12:17 EDT 2021

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proposed

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#17 by Michel Marcus at Fri Oct 22 02:58:08 EDT 2021

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#16 by Michel Marcus at Fri Oct 22 02:58:04 EDT 2021

FORMULA

a(n) = 2*floor((n-1)^2/4) + 3*ceiling(n^2/2) (conjectured). _- _Ralf Stephan_, Jan 13 2014

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#15 by N. J. A. Sloane at Sun Jan 26 12:21:17 EST 2014

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#14 by N. J. A. Sloane at Sun Jan 26 12:21:14 EST 2014

NAME

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

COMMENTS

Let point points 1, 2, 3 & 4 be placed on a straight line at interval 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.

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#13 by N. J. A. Sloane at Sat Jan 18 13:19:12 EST 2014

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#12 by Colin Barker at Thu Jan 16 11:37:22 EST 2014

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#11 by Colin Barker at Thu Jan 16 11:37:07 EST 2014

FORMULA

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

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#10 by Joerg Arndt at Mon Jan 13 11:38:20 EST 2014

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proposed

approved