A392416 Number of partitions of the vertices of the n X 3 grid graph into total dominating sets.

1, 3, 15, 33, 187, 723, 3265, 14451, 63707, 282753, 1249731, 5531139, 24469121, 108250899, 478918091, 2118744609, 9373518211, 41469120051, 183462579393, 811652664051, 3590813514139, 15886035617793, 70281041695555, 310928730092451, 1375572596332481, 6085638870654099

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-5,-13,12,45,-70,26,12,-20,8)

Formula

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).

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)).

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

Crossrefs

Row 3 of A392413.

Cf. A203280, A392415.

Sequence in context: A031091 A211441 A086380 * A324303 A009261 A372735

Adjacent sequences: A392413 A392414 A392415 * A392417 A392418 A392419

Keyword

nonn,easy

Author

Andrew Howroyd, Jan 11 2026

Status

approved