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!)
A308591 Number of minimal total dominating sets in the (2n-1)-triangular snake graph. 1
0, 3, 5, 7, 14, 22, 42, 70, 127, 218, 388, 675, 1191, 2083, 3663, 6420, 11275, 19777, 34716, 60912, 106904, 187592, 329213, 577716, 1013834, 1779141, 3122189, 5479045, 9615069, 16873254, 29610513, 51962811, 91188394, 160024458, 280823366, 492810634, 864822395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Total Dominating Set

Eric Weisstein's World of Mathematics, Triangular Snake Graph

Index entries for linear recurrences with constant coefficients, signature (0,2,1,1,1).

FORMULA

From Andrew Howroyd, Sep 08 2019: (Start)

a(n) = 2*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n > 7.

G.f.: x^2*(3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)).

(End)

MATHEMATICA

Join[{0, 3}, Table[((3 - 5 n) (-1)^n + RootSum[-1 + # - 2 #^2 + #^3 &, -2 #^n + 249 #^(n + 1) + 7 #^(n + 2) &]/23)/25, {n, 3, 20}]] (* Eric W. Weisstein, Sep 19 2021 *)

Join[{0, 3}, LinearRecurrence[{0, 2, 1, 1, 1}, {5, 7, 14, 22, 42}, 20]] (* Eric W. Weisstein, Sep 19 2021 *)

CoefficientList[Series[x (-3 - 5 x - x^2 - x^3 + x^5)/((1 + x)^2 (-1 + 2 x - x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 19 2021 *)

PROG

(PARI) concat([0], Vec((3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)) + O(x^40))) \\ Andrew Howroyd, Sep 08 2019

CROSSREFS

Sequence in context: A114980 A024372 A295717 * A309832 A319784 A346503

Adjacent sequences:  A308588 A308589 A308590 * A308592 A308593 A308594

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 09 2019

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Sep 08 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)