A392416 - OEIS

%I #8 May 28 2026 23:21:38

%S 1,3,15,33,187,723,3265,14451,63707,282753,1249731,5531139,24469121,

%T 108250899,478918091,2118744609,9373518211,41469120051,183462579393,

%U 811652664051,3590813514139,15886035617793,70281041695555,310928730092451,1375572596332481,6085638870654099

%N Number of partitions of the vertices of the n X 3 grid graph into total dominating sets.

%H Andrew Howroyd, <a href="/A392416/b392416.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5,-13,12,45,-70,26,12,-20,8)

%F a(n) = 6*a(n-1) - 5*a(n-2) - 13*a(n-3) + 12*a(n-4) + 45*a(n-5) - 70*a(n-6) + 26*a(n-7) + 12*a(n-8) - 20*a(n-9) + 8*a(n-10).

%F G.f.: x*(1 - 3*x + 2*x^2 - 29*x^3 + 91*x^4 - 120*x^5 + 46*x^6 + 20*x^7 - 44*x^8 + 24*x^9)/((1 - x)*(1 - 5*x + 3*x^2 - 2*x^3)*(1 - 3*x^2 + 10*x^4 - 4*x^6)).

%F a(n) = A203280(n)/2 + 1.

%Y Row 3 of A392413.

%Y Cf. A203280, A392415.

%K nonn,easy

%O 1,2

%A _Andrew Howroyd_, Jan 11 2026