%I #7 Feb 03 2018 16:37:41
%S 1,4,8,12,76,140,204,1228,2252,3276,19660,36044,52428,314572,576716,
%T 838860,5033164,9227468,13421772,80530636,147639500,214748364,
%U 1288490188,2362232012,3435973836,20615843020,37795712204,54975581388,329853488332,604731395276
%N a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 12, a(4) = 76.
%C Conjecture: a(n) = least positive whose base-4 down-variation is n; see column 1 of A297552.
%H Clark Kimberling, <a href="/A297555/b297555.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,16,-16)
%F a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 12, a(4) = 76.
%F G.f.: (1 + 3 x + 4 x^2 - 12 x^3 + 16 x^4)/(1 - x - 16 x^3 + 16 x^4)
%t Join[{1}, LinearRecurrence[{1, 0, 16, -16}, {4, 8, 12, 76}, 40]]
%Y Cf. A297552.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jan 21 2018