A347629 Number of minimum dominating sets in the n-pan graph (for n > 2).

2, 1, 1, 4, 2, 1, 7, 3, 1, 11, 4, 1, 16, 5, 1, 22, 6, 1, 29, 7, 1, 37, 8, 1, 46, 9, 1, 56, 10, 1, 67, 11, 1, 79, 12, 1, 92, 13, 1, 106, 14, 1, 121, 15, 1, 137, 16, 1, 154, 17, 1, 172, 18, 1, 191, 19, 1, 211, 20, 1, 232, 21, 1, 254, 22, 1, 277, 23, 1, 301, 24

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=1..71.

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Eric Weisstein's World of Mathematics, Pan Graph

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Formula

a(n) = 1 for n = 0 (mod 3)

(n^2+7*n+28)/18 for n = 1 (mod 3)

(n+1)/3 for n = 2 (mod 3).

a(n) = 3*a(n-3)-3*a(n-6)+a(n-9) for n>9.

G.f.: -x*(2 + x + x^2 - 2*x^3 - x^4 - 2*x^5 + x^6 + x^8)/((-1 + x)^3*(1 + x + x^2)^3).

Mathematica

Table[Piecewise[{{1, Mod[n, 3] == 0}, {(28 + 7 n + n^2)/18, Mod[n, 3] == 1}, {(n + 1)/3, Mod[n, 3] == 2}}], {n, 20}]
LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {2, 1, 1, 4, 2, 1, 7, 3, 1}, 20]
CoefficientList[Series[-(2 + x + x^2 - 2 x^3 - x^4 - 2 x^5 + x^6 + x^8)/((-1 + x)^3 (1 + x + x^2)^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A156861 A122773 A029268 * A176452 A244581 A064191

Adjacent sequences: A347626 A347627 A347628 * A347630 A347631 A347632

Keyword

nonn

Author

Eric W. Weisstein, Sep 09 2021

Status

approved