cp's OEIS Frontend

A036826 a(n) = A036800(n)/2.

%I A036826 #33 Sep 08 2022 08:44:52
%S A036826 0,1,9,45,173,573,1725,4861,13053,33789,84989,208893,503805,1196029,
%T A036826 2801661,6488061,14876669,33816573,76283901,170917885,380633085,
%U A036826 843055101,1858076669,4076863485,8908701693,19394461693,42077257725,90999619581,196226318333
%N A036826 a(n) = A036800(n)/2.
%C A036826 Binomial transform of A054569 (with leading 0). Partial sums of A014477 (with leading 0). - _Paul Barry_, Jun 11 2003
%C A036826 This sequence is related to A000337 by a(n) = n*A000337(n) - Sum_{i=0..n-1} A000337(i). - _Bruno Berselli_, Mar 06 2012
%H A036826 Bruno Berselli, <a href="/A036826/b036826.txt">Table of n, a(n) for n = 0..1000</a>
%H A036826 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8).
%F A036826 From _Paul Barry_, Jun 11 2003: (Start)
%F A036826 G.f.: x*(1+2*x)/((1-x)*(1-2*x)^3).
%F A036826 a(n) = 2^n*(n^2-2*n+3) - 3.
%F A036826 a(n) = Sum_{k=0..n} k^2*2^(k-1). (End)
%F A036826 a(n) = 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4). - _Harvey P. Dale_, Mar 04 2015
%F A036826 E.g.f.: -3*exp(x) + (3 -2*x +4*x^2)*exp(2*x). - _G. C. Greubel_, Mar 31 2021
%p A036826 A036826:= n-> 2^n*(3-2*n+n^2) -3; seq(A036826(n), n=0..30); # _G. C. Greubel_, Mar 31 2021
%t A036826 LinearRecurrence[{7,-18,20,-8}, {0,1,9,45}, 29] (* _Bruno Berselli_, Mar 06 2012 *)
%o A036826 (Magma) m:=28; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)/((1-x)*(1-2*x)^3))); // _Bruno Berselli_, Mar 06 2012
%o A036826 (PARI) for(n=0, 28, print1(2^n*(n^2-2*n+3)-3", ")); \\ _Bruno Berselli_, Mar 06 2012
%o A036826 (Sage) [2^n*(3-2*n+n^2) -3 for n in (0..30)] # _G. C. Greubel_, Mar 31 2021
%Y A036826 Cf. A000337, A014477, A036800, A054569, A209359.
%K A036826 nonn,easy
%O A036826 0,3
%A A036826 _N. J. A. Sloane_