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A160791 First differences of A160790. 5

%I

%S 1,1,2,3,3,6,4,10,5,15,6,21,7,28,8,36,9,45,10,55,11,66,12,78,13,91,14,

%T 105,15,120,16,136,17,153,18,171,19,190,20,210,21,231,22,253,23,276,

%U 24,300,25,325,26,351,27,378,28,406,29,435,30,465

%N First differences of A160790.

%H G. C. Greubel, <a href="/A160791/b160791.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).

%F From _R. J. Mathar_, Feb 09 2010: (Start)

%F a(2n+1) = n+1 and a(2n) = A000217(n) with a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).

%F G.f.: x*(1+x-x^2)/(1-x^2)^3. (End)

%F a(n) = (n^2+6*n+4+(n^2-2*n-4)*(-1)^n)/16. - _Luce ETIENNE_, Mar 31 2015

%F E.g.f.: (x*(x+4)*cosh(x) + (3*x+4)*sinh(x))/8. - _G. C. Greubel_, Apr 26 2018

%t Riffle[Range[30], Range[30] (Range[30] + 1)/2] (* _Bruno Berselli_, Jul 15 2013 *)

%t LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 1, 2, 3, 3, 6}, 60] (* _Vincenzo Librandi_, Apr 02 2015 *)

%o (PARI) Vec(x*(1+x-x^2)/(1-x^2)^3 + O(x^80)) \\ _Michel Marcus_, Apr 01 2015

%o (MAGMA) [(n^2+6*n+4+(n^2-2*n-4)*(-1)^n)/16: n in [1..70]]; // _Vincenzo Librandi_, Apr 02 2015

%Y Cf. A160791, A160792, A160793.

%K easy,nonn

%O 1,3

%A _Omar E. Pol_, May 29 2009

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)