%I #14 Apr 15 2018 12:20:56
%S 1,4,19,91,427,1963,8875,39595,174763,764587,3320491,14330539,
%T 61516459,262843051,1118481067,4742359723,20043180715,84467690155,
%U 355050629803,1488921995947,6230565890731,26021775190699,108485147273899
%N a(n) = n * 4^(n-1) + (2*4^n + 1) / 3.
%C Binomial transform of A064017.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F G.f.: (1-5x+7x^2)/((1-x)(1-4x)^2).
%F a(n) = A002697(n) + A007583(n).
%t LinearRecurrence[{9,-24,16},{1,4,19},30] (* _Harvey P. Dale_, Apr 15 2018 *)
%o (PARI) a(n) = my(p4 = 1<<(2*n)); n * p4 / 4 + (2*p4 + 1) / 3 \\ _David A. Corneth_, Apr 15 2018
%Y Cf. A002697, A007583, A064017.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 05 2003
%E Name clarified by _David A. Corneth_, Apr 15 2018