A297443 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.

1, 3, 6, 11, 20, 33, 60, 101, 182, 303, 546, 911, 1640, 2733, 4920, 8201, 14762, 24603, 44286, 73811, 132860, 221433, 398580, 664301, 1195742, 1992903, 3587226, 5978711, 10761680, 17936133, 32285040, 53808401, 96855122, 161425203, 290565366, 484275611

Offset

0,2

Comments

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

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,3,-3)

Formula

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.

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A297440.

Sequence in context: A320850 A180086 A116365 * A185083 A208851 A182845

Adjacent sequences: A297440 A297441 A297442 * A297444 A297445 A297446

Keyword

nonn,easy

Author

Clark Kimberling, Jan 21 2018

Status

approved