login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237930 a(n) = 3^(n+1) + (3^n-1)/2. 7
3, 10, 31, 94, 283, 850, 2551, 7654, 22963, 68890, 206671, 620014, 1860043, 5580130, 16740391, 50221174, 150663523, 451990570, 1355971711, 4067915134, 12203745403, 36611236210, 109833708631, 329501125894, 988503377683, 2965510133050, 8896530399151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n-1) agrees with the graph radius of the n-Sierpinski carpet graph for n = 2 to at least n = 5. See A100774 for the graph diameter of the n-Sierpinski carpet graph.

The inverse binomial transform gives 3, 7, 14, 28, 56,... i.e., A005009 with a leading 3. - R. J. Mathar, Jan 08 2020

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Graph Radius

Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph

Index entries for linear recurrences with constant coefficients, signature (4, -3).

FORMULA

G.f.: (3-2*x)/((1-x)*(1-3*x)).

a(n) = A000244(n+1) + A003462(n).

a(n) = 3*a(n-1) + 1 for n>0, a(0)=3. (Note that if a(0) were 1 in this recurrence we would get A003462, if it were 2 we would get A060816. - N. J. A. Sloane, Dec 06 2019)

a(n) = 4*a(n-1) - 3*a(n-2) for n>1, a(0)=3, a(1)=10.

a(n) = 2*a(n-1) + 3*a(n-2) + 2 for n>1.

a(n) = A199109(n) - 1.

a(n) = (7*3^n - 1)/2. - Eric W. Weisstein, Mar 13 2018

EXAMPLE

Ternary....................Decimal

10...............................3

101.............................10

1011............................31

10111...........................94

101111.........................283

1011111........................850

10111111......................2551

101111111.....................7654, etc.

MATHEMATICA

(* Start from Eric W. Weisstein, Mar 13 2018 *)

Table[(7 3^n - 1)/2, {n, 0, 20}]

(7 3^Range[0, 20] - 1)/2

LinearRecurrence[{4, -3}, {10, 31}, {0, 20}]

CoefficientList[Series[(3 - 2 x)/((x - 1) (3 x - 1)), {x, 0, 20}], x]

(* End *)

PROG

(PARI) Vec((3 - 2*x) / ((1 - x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Nov 27 2019

(MAGMA) [3^(n+1) + (3^n-1)/2: n in [0..40]]; // Vincenzo Librandi, Jan 09 2020

CROSSREFS

Cf. A000244, A003462, A005032 (first differences), A060816, A199109, A329774.

Sequence in context: A212031 A033121 A180432 * A192337 A106517 A055217

Adjacent sequences:  A237927 A237928 A237929 * A237931 A237932 A237933

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Feb 16 2014

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 April 7 03:42 EDT 2020. Contains 333292 sequences. (Running on oeis4.)