The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A164900 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A164900

a(2n) = 4*n*(n+1) + 3; a(2n+1) = 2*n*(n+2) + 3.
(history; published version)

#36 by Jon E. Schoenfield at Tue Jul 07 06:15:54 EDT 2015

STATUS

editing

proposed

#35 by Jon E. Schoenfield at Tue Jul 07 06:15:51 EDT 2015

NAME

a(2n) = 4*n*(n+1) + 3. ; a(2n+1) = 2*n*(n+2) + 3.

FORMULA

a(2n) = A164897(n). ; a(2n+1) = A058331(n+1).

STATUS

proposed

editing

#34 by Michel Marcus at Tue Jul 07 04:08:38 EDT 2015

STATUS

editing

proposed

#33 by Michel Marcus at Tue Jul 07 04:08:18 EDT 2015

COMMENTS

a(n) = largest odd divisor of A059100(n+1). Proof: Observe that A164900a(2n) = A059100(2n+1) and A164900a(2n+1) = (A059100(2n+2))/2 and note that (A059100(m))/2 is odd for even m. - Jeremy Gardiner, Aug 25 2013.

a(n) is also the denominator of the (n+1)-st- largest circle in a special case of the Pappus chain inspired by the Yin-Yang symbol. See illustration in the links. - Kival Ngaokrajang, Jun 20 2015

STATUS

proposed

editing

#32 by Derek Orr at Sat Jun 27 14:26:13 EDT 2015

STATUS

editing

proposed

#31 by Derek Orr at Sat Jun 27 14:26:07 EDT 2015

PROG

(PARI) vector(100, n, n--; (1/4)*((-1)^n+3)*(n^2+2*n+3)) \\ Derek Orr, Jun 27 2015

STATUS

proposed

editing

#30 by Jon E. Schoenfield at Sat Jun 20 02:04:23 EDT 2015

STATUS

editing

proposed

Discussion

Sat Jun 20

10:03

Kival Ngaokrajang: Dear all, Thank you for comment & editting.

#29 by Jon E. Schoenfield at Sat Jun 20 02:04:00 EDT 2015

COMMENTS

a(n) is also the denominator that would be of the (n+1)st-largest circle radius in a special case of The the Pappus chain which inspired by the Yin-Yang symbol. See illustration in the links. - Kival Ngaokrajang, Jun 20 2015

STATUS

proposed

editing

Discussion

Sat Jun 20

02:04

Jon E. Schoenfield: Kival -- are these wording changes okay?

#28 by Michel Marcus at Sat Jun 20 00:43:26 EDT 2015

STATUS

editing

proposed

#27 by Michel Marcus at Sat Jun 20 00:43:16 EDT 2015

LINKS

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1)