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A061925 a(n) = ceiling(n^2/2) + 1. 16
1, 2, 3, 6, 9, 14, 19, 26, 33, 42, 51, 62, 73, 86, 99, 114, 129, 146, 163, 182, 201, 222, 243, 266, 289, 314, 339, 366, 393, 422, 451, 482, 513, 546, 579, 614, 649, 686, 723, 762, 801, 842, 883, 926, 969, 1014, 1059, 1106, 1153, 1202, 1251, 1302, 1353, 1406 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n+1) gives index of the first occurrence of n in A100795. - Amarnath Murthy, Dec 05 2004

First term in each group in A074148. - Amarnath Murthy, Aug 28 2002

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = a(n-1) + 2*floor((n-1)/2) + 1 = A061926(3, k) = 2*A002620(n+1) - (n-1) = A000982(n) + 1.

a(2n) = a(2n-1) + 2n - 1 = 2*n^2 + 1 = A058331(n).

a(2n+1) = a(2n) + 2n + 1 = 2*(n^2 + n + 1) = A051890(n+1).

a(n) = floor((n^2+3)/2). - Gary Detlefs, Feb 13 2010

From R. J. Mathar, Feb 19 2010: (Start)

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

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

a(n) = (2*n^2 - (-1)^n + 5)/4. - Bruno Berselli, Sep 29 2011

a(n) = A007590(n+1) - n + 1. - Wesley Ivan Hurt, Jul 15 2013

a(n) + a(n+1) = A027688(n). a(n+1) - a(n) = A109613(n). - R. J. Mathar, Jul 20 2013

MAPLE

seq(floor((n^2+3)/2), n=0..25); # Gary Detlefs, Feb 13 2010

MATHEMATICA

Table[Ceiling[n^2/2]+1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011 *)

PROG

(PARI) { for (n=0, 1000, write("b061925.txt", n, " ", ceil(n^2/2) + 1) ) } \\ Harry J. Smith, Jul 29 2009

CROSSREFS

Cf. A100795, A074147-A074149.

Sequence in context: A127719 A074150 A261243 * A073736 A101593 A226893

Adjacent sequences:  A061922 A061923 A061924 * A061926 A061927 A061928

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, May 17 2001

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 09 2007

STATUS

approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)