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A142463 a(n) = 2*n^2 + 2*n - 1. 27
-1, 3, 11, 23, 39, 59, 83, 111, 143, 179, 219, 263, 311, 363, 419, 479, 543, 611, 683, 759, 839, 923, 1011, 1103, 1199, 1299, 1403, 1511, 1623, 1739, 1859, 1983, 2111, 2243, 2379, 2519, 2663, 2811, 2963, 3119, 3279, 3443, 3611, 3783, 3959, 4139, 4323, 4511, 4703, 4899, 5099 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All entries are odd.

Essentially the same as A132209

Numbers n such that 2n+3 is square. - Vincenzo Librandi, Nov 25 2010

First diagonal of A144562. - Vincenzo Librandi, Nov 25 2010

a(n) = - A188653(2*n+1). - Reinhard Zumkeller, Apr 13 2011

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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

FORMULA

a(n) = a(n-1) + 4*n.

From Paul Barry, Nov 03 2009: (Start)

G.f.: (1 - 6x + x^2)/(1-x)^3.

a(n) = 4*C(n+1,2) - 1. (End)

a(n) = 3*sum(k^5,k=1..n)/sum(k^3,k=1..n), n>0. - Gary Detlefs, Oct 18 2011

a(n) = (A005408(n)^2 - 3)/2. - Zhandos Mambetaliyev, Feb 11 2017

MATHEMATICA

a[0] = -1; a[n_] := a[n] = a[n - 1] + n; Table[a[n], {n, 0, 30}]; f[n_] := 4*a[n] + 3; Table[f[n], {n, 0, 50}] (* Roger L. Bagula and Gary W. Adamson, Oct 20 2008 *)

Array[ -#*(2-#*2)-1&, 5!, 1] (* Vladimir Joseph Stephan Orlovsky, Dec 21 2008 *)

PROG

(MAGMA) [2*n^2+2*n-1: n in [0..100]]

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

CROSSREFS

Cf. A132209, A000096.

Sequence in context: A119173 A106201 A132209 * A086497 A121509 A096071

Adjacent sequences:  A142460 A142461 A142462 * A142464 A142465 A142466

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Sep 19 2008

EXTENSIONS

Edited by the Associate Editors of the OEIS, Sep 02 2009

STATUS

approved

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Last modified March 27 06:40 EDT 2017. Contains 284144 sequences.