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A130883 a(n) = 2*n^2 - n + 1. 21
1, 2, 7, 16, 29, 46, 67, 92, 121, 154, 191, 232, 277, 326, 379, 436, 497, 562, 631, 704, 781, 862, 947, 1036, 1129, 1226, 1327, 1432, 1541, 1654, 1771, 1892, 2017, 2146, 2279, 2416, 2557, 2702, 2851, 3004, 3161, 3322, 3487, 3656, 3829 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Maximum number of regions determined by n bent lines (angular sectors). See GKP Reference.

a(n) = A128918(2*n). - Reinhard Zumkeller, Oct 27 2013

a(n)*Pi is the total length of half circle spiral after n rotations. It is formed as irregular spiral with two center points. At the 2nd stage, there are two alternatives: (1) select 2nd half circle radius, r2  = 2, the sequence will be A014105 or (2) select r2 = 0, the sequence will be A130883. See illustration in links. - Kival Ngaokrajang, Jan 19 2014

A128218(a(n)) = 2*n+1 and A128218(m) != 2*n+1 for m < a(n). - Reinhard Zumkeller, Jun 20 2015

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 2nd ed., Addison-Wesley, Reading, MA, 1994, pp7-8.

LINKS

Table of n, a(n) for n=0..44.

Guo-Niu Han, Enumeration of Standard Puzzles

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

Kival Ngaokrajang, Illustration of irregular spirals (center points: 1, 2)

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

FORMULA

a(n) = a(n-1)+4*n-3 for n>0, a(0)=1. - Vincenzo Librandi, Nov 23 2010

a(n) = A000124(2*n)-2*n. - Geoffrey Critzer, Mar 30 2011

O.g.f.:(4*x^2-x+1)/(1-x)^3. - Geoffrey Critzer, Mar 30 2011

a(n) = 2*a(n-1)-a(n-2)+4. - Eric Werley, Jun 27 2011

a(0)=1, a(1)=2, a(2)=7; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 20 2011

MATHEMATICA

a[n_]:=2*n^2-n+1; (* or *) Array[ -#*(1-#*2)+1&, 5!, 0] (* Vladimir Joseph Stephan Orlovsky, Dec 21 2008 *)

LinearRecurrence[{3, -3, 1}, {1, 2, 7}, 50] (* Harvey P. Dale, Jul 20 2011 *)

PROG

(Haskell)

a130883 = a128918 . (* 2)  -- Reinhard Zumkeller, Oct 27 2013

(PARI) a(n)=2*n^2-n+1 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000124, A084849, A128218, A128918.

Cf. A270109. [From Bruno Berselli, Mar 17 2016]

Sequence in context: A048231 A070169 A162420 * A005581 A064468 A225311

Adjacent sequences:  A130880 A130881 A130882 * A130884 A130885 A130886

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, Jul 26 2007

STATUS

approved

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Last modified December 4 02:25 EST 2016. Contains 278745 sequences.