The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A297443 revision #2

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

(list; graph; refs; listen; history; text; internal format)

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

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]]