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A114949 a(n) = n^2 + 6. 18
6, 7, 10, 15, 22, 31, 42, 55, 70, 87, 106, 127, 150, 175, 202, 231, 262, 295, 330, 367, 406, 447, 490, 535, 582, 631, 682, 735, 790, 847, 906, 967, 1030, 1095, 1162, 1231, 1302, 1375, 1450, 1527, 1606, 1687, 1770, 1855, 1942, 2031, 2122, 2215, 2310, 2407, 2506 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

2/a(n) = R(n)/r, n >= 0, with R(n) the n-th radius of the counterclockwise Pappus chain of the arbelos with semicircle radii r, r1 = 2r/3, r2 = r - r1 = r/3. See the MathWorld link for such a Pappus chain. The clockwise chain companion has circle radii R'(n)/r = 2/A222465(n), n>=0. - Wolfdieter Lang, Mar 01 2013

(5n)*a(n) = (n-2)^3 + (n-1)^3 + n^3 + (n+1)^3 + (n+2)^3. - Bruno Berselli, May 12 2014

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Pappus chain

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 3*a(n - 1) - 3*a(n - 2) + a(n - 3). - R. J. Mathar, May 17 2009

G.f.: -(6 - 11*x + 7*x^2)/(x - 1)^3. - R. J. Mathar, May 17 2009

a(n) = 2*n + a(n - 1) - 1, with n>0, a(0)=6. - Vincenzo Librandi, Nov 13 2010

a(n) = A000290(n) + 6. - Omar E. Pol, Mar 02 2013

For n>=1, a(n) = (A016742(n) + A082044(n) - 1) / A000290(n). - Bruce J. Nicholson, Apr 19 2017

EXAMPLE

The arbelos chain defined in a comment above has circle radii [1/3, 2/7, 1/5, 2/15, 1/11, 2/31, 1/21, 2/55, 1/35, 2/87, 1/53,...], for n >= 0. - Wolfdieter Lang, Mar 01 2013

MAPLE

A114949:=n->n^2+6: seq(A114949(n), n=0..100); # Wesley Ivan Hurt, Apr 28 2017

MATHEMATICA

Range[0, 49]^2 + 6 (* Alonso del Arte, Jan 30 2013 *)

PROG

(PARI) g(n) = for(x=1, n, y=x^2+6; print1(y", "))

CROSSREFS

Cf. A002522, A059100, A087475, A117619, A117950, A117951, A114964 (see comment), A222465, A016742, A082044, A000290.

Sequence in context: A287386 A287803 A216348 * A081359 A117618 A015825

Adjacent sequences:  A114946 A114947 A114948 * A114950 A114951 A114952

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, Feb 21 2006

STATUS

approved

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Last modified February 19 03:25 EST 2018. Contains 299330 sequences. (Running on oeis4.)