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A014848 n^2 - floor( n/2 ). 8
0, 1, 3, 8, 14, 23, 33, 46, 60, 77, 95, 116, 138, 163, 189, 218, 248, 281, 315, 352, 390, 431, 473, 518, 564, 613, 663, 716, 770, 827, 885, 946, 1008, 1073, 1139, 1208, 1278, 1351, 1425, 1502, 1580, 1661, 1743, 1828, 1914, 2003, 2093, 2186, 2280, 2377, 2475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Quasipolynomial of order 2. - Charles R Greathouse IV, Jan 19 2012

The binomial transform is 0, 1, 5, 20,... which is A084850 with offset 1. - R. J. Mathar, Nov 26 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

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

a(n) = (2*n*(2*n-1)-(-1)^n+1)/4. - Bruno Berselli, Feb 17 2011

a(n) = round(n/(exp(1/n) - 1)), n > 0. - Richard R. Forberg, Nov 14 2014

MAPLE

A014848:=n->n^2 - floor(n/2); seq(A014848(n), n=0..50); # Wesley Ivan Hurt, Oct 11 2013

MATHEMATICA

Table[n^2-Floor[n/2], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

PROG

(PARI) a(n)=n^2-n\2

(MAGMA) [n^2-Floor(n/2) : n in [0..50]]; // Wesley Ivan Hurt, Nov 14 2014

CROSSREFS

Cf. A033991(n)=a(2n), A033951(n)=a(2n+1), A042963 (first differences).

Sequence in context: A219930 A022947 A098762 * A140479 A264689 A146158

Adjacent sequences:  A014845 A014846 A014847 * A014849 A014850 A014851

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 16 20:08 EST 2019. Contains 329204 sequences. (Running on oeis4.)