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%I #22 Nov 23 2018 22:14:26
%S 1,4,14,31,55,86,124,169,221,280,346,419,499,586,680,781,889,1004,
%T 1126,1255,1391,1534,1684,1841,2005,2176,2354,2539,2731,2930,3136,
%U 3349,3569,3796,4030,4271,4519,4774,5036
%N Binomial transform of [1, 3, 7, 0, 0, 0, ...].
%H Derek Kinsella, <a href="http://www.90thkilmacudscouts.com/maths/circles_lines_soln.html">Plane division by lines and circles</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A007318 * [1, 3, 7, 0, 0, 0, ...].
%F O.g.f.: x*(1 + x + 5x^2)/(1-x)^3. - _R. J. Mathar_, May 06 2008
%F a(n) = 7*n^2/2 - 15*n/2 + 5 = 3*a(n-1) - 3*a(n-2) + a(n-3). - _R. J. Mathar_, Jul 31 2009
%F a(n) = a(n-1) + 7*n - 11 (with a(1)=1). - _Vincenzo Librandi_, Nov 24 2010
%e a(4) = 31 = (1, 3, 3, 1) dot (1, 3, 7, 0) = (1 + 9 + 21 + 0).
%t s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 265, 7}]; lst # _Zerinvary Lajos_, Jul 11 2009
%o (PARI) a(n)=n*(7*n-15)/2+5 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, May 03 2008
%E More terms from _R. J. Mathar_, May 06 2008
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