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 A135042 Binomial transform of [1, 1, 2, 0, -2, 4, -6, 8, -10, 12,...]. 2

%I

%S 1,2,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,

%T 110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,

%U 195,200,205,210,215,220,225,230,235,240,245,250

%N Binomial transform of [1, 1, 2, 0, -2, 4, -6, 8, -10, 12,...].

%C A007318 * [1, 1, 2, 0, -2, 4, -6, 8, -10, 12,...].

%C Sum of antidiagonal terms of the following arithmetic array:

%C 1, 1, 1, 1, 1,...

%C 1, 3, 5, 7, 9,...

%C 1, 4, 7, 10, 13,...

%C ...

%H G. C. Greubel, <a href="/A135042/b135042.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1) -a(n-2), n>3. - _R. J. Mathar_, Apr 21 2010, corrected Sep 02 2010

%F G.f.: (1 + 2*x^2 + 2*x^3)/(1-x)^2. - _Colin Barker_, Feb 01 2012

%F From _G. C. Greubel_, Sep 18 2016: (Start)

%F a(n) = 5*(n + 1) for n>=3.

%F E.g.f.: 5*(-1 + x)*exp(x) + 2*(3 + x). (End)

%e a(4) = 10 = (1, 3, 3, 1) dot (1, 1, 2, 0) = (1 + 3 + 6 + 0).

%e a(4) = 10 = (4 + 5 + 1).

%t Join[{1,2}, Table[5*(n-1), {n,2,25}]] (* _G. C. Greubel_, Sep 18 2016 *)

%o (MAGMA) [1,2] cat [5*(n-1): n in [2..50]]; // _Vincenzo Librandi_, Sep 18 2016

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, May 10 2008

%E Offset corrected and one 75 replaced by 65 - _R. J. Mathar_, Apr 21 2010

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Last modified August 13 02:52 EDT 2020. Contains 336441 sequences. (Running on oeis4.)