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A302650 Number of minimal total dominating sets in the n-barbell graph. 1
1, 1, 6, 28, 85, 201, 406, 736, 1233, 1945, 2926, 4236, 5941, 8113, 10830, 14176, 18241, 23121, 28918, 35740, 43701, 52921, 63526, 75648, 89425, 105001, 122526, 142156, 164053, 188385, 215326, 245056, 277761, 313633, 352870, 395676, 442261, 492841, 547638, 606880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Extended to a(1)-a(2) using the formula/recurrence.

LINKS

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Barbell Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

a(n) = (2 + (n - 3)*n*(n + 1)/4)*n.

G.f.: x*(-1 + 4*x - 11*x^2 + 2*x^3)/(-1 + x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

MATHEMATICA

Table[(2 + (n - 3) n (n + 1)/4) n, {n, 20}]

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 6, 28, 85}, 20]

CoefficientList[Series[(-1 + 4 x - 11 x^2 + 2 x^3)/(-1 + x)^5, {x, 0, 20}], x]

CROSSREFS

Sequence in context: A279915 A300906 A222198 * A055711 A141255 A091321

Adjacent sequences:  A302647 A302648 A302649 * A302651 A302652 A302653

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 11 2018

STATUS

approved

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Last modified November 18 22:39 EST 2019. Contains 329305 sequences. (Running on oeis4.)