The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#3 by Clark Kimberling at Sun Jan 21 08:07:59 EST 2018

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.: (3 + 3 x - x^2 + 3 x^3 - 6 x^4)/(1 - x - 2 x^2 + 2 x^3 - 3 x^4 +

3 x^5)

#2 by Clark Kimberling at Sun Jan 21 07:56:48 EST 2018

NAME

allocated for Clark Kimberling

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.

DATA

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

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,3,-3)

FORMULA

If n = (1 mod 4) or n = (1 mod 4), then a(n) = 3*a(n-2); otherwise, a(n) = 3*a(n-2) + 2.

MATHEMATICA

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

CROSSREFS

Cf. A297440.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Jan 21 2018

STATUS

approved