A297443 - OEIS

%I #13 Feb 03 2018 16:37:29

%S 1,3,6,11,20,33,60,101,182,303,546,911,1640,2733,4920,8201,14762,

%T 24603,44286,73811,132860,221433,398580,664301,1195742,1992903,

%U 3587226,5978711,10761680,17936133,32285040,53808401,96855122,161425203,290565366,484275611

%N a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - 3*a(n-5), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 11, a(4) = 20, a(5) = 33.

%C Conjecture:  a(n) = least positive whose base-3 total variation is n; see A297440.

%H Clark Kimberling, <a href="/A297443/b297443.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,3,-3)

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - 3*a(n-5), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 11, a(4) = 20, a(5) = 33.

%F G.f.: (1 + 2*x + x^2 + x^3 - 3*x^5) / ((1 - x)*(1 + x^2)*(1 - 3*x^2)). - Corrected by _Colin Barker_, Jan 21 2018

%t Join[{1}, LinearRecurrence[{1, 2, -2, 3, -3}, {3, 6, 11, 20, 33}, 40]]

%o (PARI) Vec((1 + 2*x + x^2 + x^3 - 3*x^5) / ((1 - x)*(1 + x^2)*(1 - 3*x^2)) + O(x^40)) \\ _Colin Barker_, Jan 21 2018

%Y Cf. A297440.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jan 21 2018