A303834 Number of total dominating sets in the n-gear graph.

3, 21, 48, 161, 473, 1476, 4553, 14241, 44688, 141081, 447153, 1422596, 4539473, 14522361, 46556048, 149508801, 480810153, 1548053316, 4988972313, 16090635281, 51928966928, 167675418921, 541639730273, 1750245266436, 5657268819873, 18289912673001

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Gear Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (4,2,-13,-6,4).

Formula

a(n) = 2*(-1)^n + 2^n*A000032(n) + A005248(n).

a(n) = 4*a(n-1) + 2*a(n-2) - 13*a(n-3) - 6*a(n-4) + 4*a(n-5).

G.f.: -x*(3+9*x-42*x^2-34*x^3+24*x^4) / ( (1+x)*(x^2-3*x+1)*(4*x^2+2*x-1) ).

Mathematica

Table[2 (-1)^n + 2^n LucasL[n] + LucasL[2 n], {n, 20}]
LinearRecurrence[{4, 2, -13, -6, 4}, {3, 21, 48, 161, 473}, 20]
CoefficientList[Series[(-3 - 9 x + 42 x^2 + 34 x^3 - 24 x^4)/(-1 + 4 x + 2 x^2 - 13 x^3 - 6 x^4 + 4 x^5), {x, 0, 20}], x]

Crossrefs

Sequence in context: A318211 A219069 A027499 * A340687 A152773 A039595

Adjacent sequences: A303831 A303832 A303833 * A303835 A303836 A303837

Keyword

nonn,easy

Author

Eric W. Weisstein, May 02 2018

Status

approved