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A185950 a(n) = 4*n^2 - n - 1. 3
-1, 2, 13, 32, 59, 94, 137, 188, 247, 314, 389, 472, 563, 662, 769, 884, 1007, 1138, 1277, 1424, 1579, 1742, 1913, 2092, 2279, 2474, 2677, 2888, 3107, 3334, 3569, 3812, 4063, 4322, 4589, 4864, 5147, 5438, 5737, 6044, 6359, 6682, 7013, 7352, 7699, 8054, 8417, 8788, 9167, 9554, 9949, 10352, 10763, 11182, 11609 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Write the sequence A023443 in a clockwise spiral. a(n) is on the y-axis.
a(n) mod 9 = period 9: repeat [8,2,4,5,5,4,2,8,4] = A182868(n+2) mod 9.
LINKS
FORMULA
a(n) = A176126(4*n-1) = A054556(n+1) - 2 = A033991(n) - 1.
a(n) = a(n-1) + 8*n - 5.
a(n) = 2*a(n-1) - a(n-2) + 8.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: ( 1-5*x-4*x^2 ) / (x-1)^3. - R. J. Mathar, Feb 10 2011
E.g.f.: (4*x^2 + 3*x - 1)*exp(x). - G. C. Greubel, Jul 23 2017
EXAMPLE
11--12--13--14--15
| |
10 1---2---3 16
| | | |
9 0-(-1) 4 17
| | |
8---7---6---5 18
MAPLE
A185950:=n->4*n^2-n-1: seq(A185950(n), n=0..100); # Wesley Ivan Hurt, Jan 30 2017
MATHEMATICA
Table[4n^2-n-1, {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {-1, 2, 13}, 60] (* Harvey P. Dale, May 22 2015 *)
PROG
(Magma)[-1-n+4*n^2: n in [0..80]]; // Vincenzo Librandi, Feb 08 2011
(PARI) a(n)=4*n^2-n-1 \\ Charles R Greathouse IV, Dec 21 2011
(Haskell)
a185950 n = (4 * n - 1) * n - 1 -- Reinhard Zumkeller, Aug 14 2013
CROSSREFS
Sequence in context: A106959 A285096 A177455 * A084828 A100512 A051474
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Feb 07 2011
STATUS
approved

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Last modified April 19 08:45 EDT 2024. Contains 371782 sequences. (Running on oeis4.)