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A099392 a(n) = floor((n^2 - 2*n + 3)/2). 13
1, 1, 3, 5, 9, 13, 19, 25, 33, 41, 51, 61, 73, 85, 99, 113, 129, 145, 163, 181, 201, 221, 243, 265, 289, 313, 339, 365, 393, 421, 451, 481, 513, 545, 579, 613, 649, 685, 723, 761, 801, 841, 883, 925, 969, 1013, 1059, 1105, 1153, 1201, 1251, 1301, 1353, 1405 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Guenther Schrack, Table of n, a(n) for n = 1..10010

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

FORMULA

a(n) = ceiling(n^2/2)-n+1. - Paul Barry, Jul 16 2006; index shifted by R. J. Mathar, Jul 29 2007

a(n) = ceiling(A002522(n-1)/2). - Branko Curgus, Sep 02 2007

From R. J. Mathar, Feb 20 2011: (Start)

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

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

a(n+1) = (3 + 2*n^2 + (-1)^n)/4. (End)

a(n) = A007590(n-1) + 1 for n >= 2. - Richard R. Forberg, Aug 01 2013

a(n) = A000217(n) - A007494(n-1). - Bui Quang Tuan, Mar 27 2015

From Guenther Schrack, Apr 17 2018: (Start)

a(n) = (2*n^2 - 4*n + 5 -(-1)^n)/4.

a(n+2) = a(n) + 2*n for n > 0.

a(n) = 2*A033683(n-1) - 1 for n > 0.

a(n) = A047838(n-1) + 2 for n > 2.

a(n) = A074148(n-1) - n + 2 for n > 1.

a(n) = A183575(n-3) + 3 for n > 3.

a(n) = 2*A290743(n-1) - 3 for n > 0.

a(n) = 2*A290743(n-2) + A109613(n-5) for n > 4.

a(n) = A074148(n) - A014601(n-1) for n > 0. (End)

MATHEMATICA

Array[Floor[(#^2 - 2 # + 3)/2] &, 54] (* or *)

Rest@ CoefficientList[Series[x (-1 + x - x^2 - x^3)/((1 + x) (x - 1)^3), {x, 0, 54}], x] (* Michael De Vlieger, Apr 21 2018 *)

PROG

(PARI) a(n)=(n^2+3)\2-n \\ Charles R Greathouse IV, Aug 01 2013

CROSSREFS

Differs from A085913 at n = 61. Apart from leading term, identical to A080827.

Cf. A001844, A058331 (bisections).

From Guenther Schrack, Apr 17 2018: (Start)

First differences: A052928.

Partial sums: A212964(n) + n for n > 0.

Also A058331 and A001844 interleaved. (End)

Sequence in context: A245302 A118028 A209974 * A080827 A200919 A213207

Adjacent sequences:  A099389 A099390 A099391 * A099393 A099394 A099395

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan following a suggestion from Luke Pebody, Oct 20 2004

STATUS

approved

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Last modified October 23 06:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)