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!)
A298823 Number of minimal total dominating sets in the n-dipyramidal graph. 1
2, 4, 9, 12, 15, 21, 21, 20, 30, 45, 44, 49, 65, 77, 98, 132, 153, 180, 247, 329, 409, 528, 690, 889, 1180, 1573, 2037, 2657, 3538, 4684, 6169, 8164, 10783, 14229, 18877, 25036, 33078, 43757, 57996, 76809, 101721, 134773, 178450, 236284, 313097, 414828, 549383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

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

FORMULA

From Andrew Howroyd, Jun 26 2018: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-7) + a(n-9) + a(n-10) - a(n-11) for n > 11.

G.f.: x*(2 + 3*x^2 - 4*x^3 - 2*x^4 - 2*x^5 - 9*x^6 - 2*x^7 + 9*x^8 + 12*x^9 - 9*x^10)/((1 - x)^2*(1 - x^2 - x^3)*(1 + x^2 - x^6)). (End)

MATHEMATICA

Table[2 n + RootSum[-1 - # + #^3 &, #^n &] + (1 + (-1)^n) RootSum[-1 - # + #^3 &, #^(-n/2) &], {n, 20}]

LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {2, 4, 9, 12, 15, 21, 21, 20, 30, 45, 44}, 20]

CoefficientList[Series[(2 + 3 x^2 - 4 x^3 - 2 x^4 - 2 x^5 - 9 x^6 - 2 x^7 + 9 x^8 + 12 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 20}], x]

PROG

(PARI) Vec((2 + 3*x^2 - 4*x^3 - 2*x^4 - 2*x^5 - 9*x^6 - 2*x^7 + 9*x^8 + 12*x^9 - 9*x^10)/((1 - x)^2*(1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50)) \\ Andrew Howroyd, Jun 26 2018

CROSSREFS

Sequence in context: A022428 A096186 A175041 * A219114 A182859 A341239

Adjacent sequences:  A298820 A298821 A298822 * A298824 A298825 A298826

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 18 2018

EXTENSIONS

a(1)-a(2) and terms a(21) and beyond from Andrew Howroyd, Jun 26 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 July 29 05:30 EDT 2021. Contains 346340 sequences. (Running on oeis4.)