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%I #35 Jan 12 2024 06:58:43
%S 3,7,18,36,61,93,132,178,231,291,358,432,513,601,696,798,907,1023,
%T 1146,1276,1413,1557,1708,1866,2031,2203,2382,2568,2761,2961,3168,
%U 3382,3603,3831,4066,4308,4557,4813,5076,5346,5623,5907,6198,6496,6801,7113,7432
%N a(n) = 3 + n/2 + 7*n^2/2.
%H Vincenzo Librandi, <a href="/A006124/b006124.txt">Table of n, a(n) for n = 0..1000</a>
%H Jonathan L. King, <a href="http://www.math.ufl.edu/~squash/">Brick tiling and monotone Boolean functions</a>
%H 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 C. L. Mallows & N. J. A. Sloane, <a href="/A006123/a006123.pdf">Emails, May 1991</a>
%H C. L. Mallows & N. J. A. Sloane, <a href="/A006123/a006123_1.pdf">Emails, Jun. 1991</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (3-2*x+6*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jul 07 2012
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 07 2012
%F a(n) = 3+A022265(n). - _R. J. Mathar_, Jan 12 2024
%t Table[3+n/2+7/2 n^2,{n,0,50}] (* _Harvey P. Dale_, Mar 21 2011 *)
%t CoefficientList[Series[(3-2*x+6*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%o (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 (PARI) a(n)=3+n/2+7*n^2/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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