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A184005 a(n) = n - 1 + ceiling(3*n^2/4); complement of A184004. 6
1, 4, 9, 15, 23, 32, 43, 55, 69, 84, 101, 119, 139, 160, 183, 207, 233, 260, 289, 319, 351, 384, 419, 455, 493, 532, 573, 615, 659, 704, 751, 799, 849, 900, 953, 1007, 1063, 1120, 1179, 1239, 1301, 1364, 1429, 1495, 1563, 1632, 1703, 1775, 1849, 1924, 2001, 2079, 2159, 2240, 2323, 2407, 2493, 2580, 2669, 2759 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

FORMULA

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

From Bruno Berselli, Jan 25 2011: (Start)

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

a(n) = (6*n^2 + 8*n - (-1)^n - 7)/8. (End)

a(n) = round((6*n^2 + 8*n - 7)/8). - Bruno Berselli, Jan 25 2011

From Paul Curtz, Feb 09 2011: (Start)

a(n) - a(n-1)  = A007494(n).

a(n) - a(n-2)  = 3*n - 1 = A016789(n-1).

a(n) - a(n-4)  = 6*n - 8 = A016957(n-2).

a(n) - a(n-8)  = 12*n - 40 = A017617(n-4).

a(n) - a(n-16) = 24*n - 176 = 8*A016789(n-8).

a(n) - a(n-32) = 48*n - 736 = 16*A016789(n-16). (End)

a(n) = n^2 - floor((n-2)^2/4). - Bruno Berselli, Jan 17 2017

a(n) = A002061(n+2) - A002620(n+4). - Anton Zakharov, May 17 2017

E.g.f.: (1/8)*(8 + (6*x^2 + 14*x -7)*exp(x) - exp(-x)). - G. C. Greubel, Jul 22 2017

MATHEMATICA

a=4/3; b=0;

Table[n+Floor[(a*n+b)^(1/2)], {n, 80}]

Table[n-1+Ceiling[(n*n-b)/a], {n, 60}]

Table[n - 1 + Ceiling[3 n^2/4], {n, 60}] (* or *) CoefficientList[ Series[x (1 + 2 x + x^2 - x^3)/((1 + x) (1 - x)^3), {x, 0, 60}], x] (* or *) Table[Round[(6 n^2 + 8 n - 7)/8], {n, 60}] (* Michael De Vlieger, Mar 23 2016 *)

LinearRecurrence[{2, 0, -2, 1}, {1, 4, 9, 15}, 60] (* Harvey P. Dale, Sep 16 2016 *)

PROG

(MAGMA) [(6*n^2 + 8*n - (-1)^n - 7)/8: n in [1..80]]; // Vincenzo Librandi, Feb 09 2011

(PARI) x='x+O('x^200); Vec(x*(1+2*x+x^2-x^3)/((1+x)*(1-x)^3)) \\ Altug Alkan, Mar 23 2016

CROSSREFS

Cf. A184004.

Sequence in context: A079423 A285283 A243536 * A194106 A004629 A065893

Adjacent sequences:  A184002 A184003 A184004 * A184006 A184007 A184008

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 08 2011

STATUS

approved

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Last modified October 18 20:10 EDT 2018. Contains 316325 sequences. (Running on oeis4.)