cp's OEIS Frontend

A340257 a(n) = 2^n * (1+n*(n+1)/2).

%I A340257 #23 Jan 19 2023 19:35:40
%S A340257 1,4,16,56,176,512,1408,3712,9472,23552,57344,137216,323584,753664,
%T A340257 1736704,3964928,8978432,20185088,45088768,100139008,221249536,
%U A340257 486539264,1065353216,2323644416,5049942016,10938744832,23622320128,50868518912,109253230592,234075717632
%N A340257 a(n) = 2^n * (1+n*(n+1)/2).
%H A340257 Alois P. Heinz, <a href="/A340257/b340257.txt">Table of n, a(n) for n = 0..1000</a>
%H A340257 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A340257 G.f.: (4*x^2-2*x+1)/(1-2*x)^3.
%F A340257 E.g.f.: exp(2*x)*(2*x^2+2*x+1).
%F A340257 a(n) = A000079(n) + A001815(n+1).
%F A340257 a(n) = A000079(n) * A000124(n).
%F A340257 a(n) = 2*a(n-1) + n*2^n = 2*a(n-1) + A036289(n), assuming a(-1) = 1/2.
%F A340257 a(n) = A340298(2^n).
%F A340257 a(n) = 2 * A087431(n) for n > 0.
%F A340257 a(n) = 4 * A007466(n) for n > 0.
%p A340257 a:= n-> 2^n*(1+n*(n+1)/2):
%p A340257 seq(a(n), n=0..30);
%t A340257 Table[2^n (1+(n(n+1))/2),{n,0,30}] (* or *) LinearRecurrence[{6,-12,8},{1,4,16},30] (* _Harvey P. Dale_, Jan 19 2023 *)
%Y A340257 Partial sums of A080929.
%Y A340257 Cf. A000079, A000124, A001787, A001815, A036289, A087431, A340298.
%K A340257 nonn
%O A340257 0,2
%A A340257 _Alois P. Heinz_, Jan 02 2021