cp's OEIS Frontend

A006124 a(n) = 3 + n/2 + 7*n^2/2.

%I A006124 #38 Dec 30 2024 14:56:58
%S A006124 3,7,18,36,61,93,132,178,231,291,358,432,513,601,696,798,907,1023,
%T A006124 1146,1276,1413,1557,1708,1866,2031,2203,2382,2568,2761,2961,3168,
%U A006124 3382,3603,3831,4066,4308,4557,4813,5076,5346,5623,5907,6198,6496,6801,7113,7432,7758
%N A006124 a(n) = 3 + n/2 + 7*n^2/2.
%H A006124 Vincenzo Librandi, <a href="/A006124/b006124.txt">Table of n, a(n) for n = 0..1000</a>
%H A006124 Jonathan L. King, <a href="http://www.math.ufl.edu/~squash/">Brick tiling and monotone Boolean functions</a>.
%H A006124 Jonathan L. King, <a href="https://arxiv.org/abs/math/9809176">A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings</a>, arXiv:math/9809176 [math.CO], 1998, page 10, row 3 of the table.
%H A006124 C. L. Mallows & N. J. A. Sloane, <a href="/A006123/a006123.pdf">Emails, May 1991</a>.
%H A006124 C. L. Mallows & N. J. A. Sloane, <a href="/A006123/a006123_1.pdf">Emails, Jun. 1991</a>.
%H A006124 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A006124 From _Vincenzo Librandi_, Jul 07 2012: (Start)
%F A006124 G.f.: (3 - 2*x + 6*x^2)/(1-x)^3.
%F A006124 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A006124 a(n) = 3 + A022265(n). - _R. J. Mathar_, Jan 12 2024
%F A006124 E.g.f.: exp(x)*(6 + 8*x + 7*x^2)/2. - _Elmo R. Oliveira_, Dec 28 2024
%t A006124 Table[3+n/2+7/2 n^2,{n,0,50}]  (* _Harvey P. Dale_, Mar 21 2011 *)
%t A006124 CoefficientList[Series[(3-2*x+6*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%o A006124 (Magma) I:=[3, 7, 18]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jul 07 2012
%o A006124 (PARI) a(n)=3+n/2+7*n^2/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A006124 Cf. A022265.
%K A006124 nonn,easy
%O A006124 0,1
%A A006124 _N. J. A. Sloane_