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A140063 Binomial transform of [1, 3, 7, 0, 0, 0, ...]. 2

%I

%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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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)