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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297445 a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3), where a(0) = 1, a(1) = 5, a(2) = 11. 2
1, 5, 11, 47, 101, 425, 911, 3827, 8201, 34445, 73811, 310007, 664301, 2790065, 5978711, 25110587, 53808401, 225995285, 484275611, 2033957567, 4358480501, 18305618105, 39226324511, 164750562947, 353036920601, 1482755066525, 3177332285411, 13344795598727 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture:  a(n) = least positive whose base-3 up-variation is n; see A297441.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,9,-9)

FORMULA

a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3) for n>2. - Corrected by Colin Barker, Jan 21 2018

G.f.: (1 + 4 x - 3 x^2)/(1 - x - 9 x^2 + 9 x^3).

a(n) = (-1 - (-3)^n + 2*3^(1+n)) / 4. - Colin Barker, Jan 21 2018

MAPLE

seq(-1/4-(-3)^n/4+3*3^n/2, n=0..40); # Robert Israel, Jan 21 2018

MATHEMATICA

LinearRecurrence[{1, 9, -9}, {1, 5, 11}, 40]]

PROG

(PARI) Vec((1 + 4*x - 3*x^2) / ((1 - x)*(1 - 3*x)*(1 + 3*x)) + O(x^40)) \\ Colin Barker, Jan 21 2018

CROSSREFS

Cf. A297442.

Sequence in context: A092358 A079029 A106953 * A149503 A149504 A149505

Adjacent sequences:  A297442 A297443 A297444 * A297446 A297447 A297448

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 21 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)