A053436 a(n) = n+1 + ceiling(n/2)*(ceiling(n/2)-1)*(ceiling(n/2)+1)/6.

2, 3, 5, 6, 10, 11, 18, 19, 30, 31, 47, 48, 70, 71, 100, 101, 138, 139, 185, 186, 242, 243, 310, 311, 390, 391, 483, 484, 590, 591, 712, 713, 850, 851, 1005, 1006, 1178, 1179, 1370, 1371, 1582, 1583, 1815, 1816, 2070, 2071, 2348, 2349, 2650, 2651

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

G. Giani, K. Strassburger, Multiple comparison procedures for optimally discriminating between good, equivalent and bad treatments with respect to a control, J. Statist. Planning Infer. 83 (No. 2, 2000), 413-440.

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

Formula

a(n) = n + 1 + A000292(ceiling(n/2)-2).

a(n) = a(n-1) +3 a(n-2) -3 a(n-3) -3 a(n-4) +3 a(n-5) +a(n-6) -a(n-7). - R. J. Mathar, Mar 11 2012

G.f.: x*(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3). - Colin Barker, Apr 02 2012

a(n) = (2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96. - Luce ETIENNE, Oct 22 2014

Mathematica

CoefficientList[Series[(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 28 2012 *)
cn[n_]:=(Times@@(Ceiling[n/2]+{1, 0, -1}))/6+n+1; Array[cn, 50] (* or *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {2, 3, 5, 6, 10, 11, 18}, 50] (* Harvey P. Dale, Mar 27 2013 *)

Prog

(Magma) [n+1 + Ceiling(n/2)*(Ceiling(n/2)-1)*(Ceiling(n/2)+1)/6: n in [1..50]]; // Vincenzo Librandi, Apr 28 2012
(PARI) for(n=1, 30, print1((2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96, ", ")) \\ G. C. Greubel, May 26 2018

Crossrefs

Cf. A000292.

Sequence in context: A024560 A000039 A302600 * A057546 A339514 A138587

Adjacent sequences: A053433 A053434 A053435 * A053437 A053438 A053439

Keyword

easy,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 11 2000

Status

approved