A286848 Number of minimal dominating sets in the grid graph P_3 X P_n.

2, 7, 16, 53, 154, 436, 1268, 3660, 10610, 30744, 89079, 258251, 748420, 2169219, 6287336, 18222901, 52817261, 153084840, 443698814, 1286012537, 3727362387, 10803344089, 31312289784, 90755170545, 263043739916, 762402920030, 2209739758798, 6404684091893

Offset: 1

Author

Andrew Howroyd, Aug 01 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Minimal Dominating Set

Crossrefs

Row 3 of A286847.

Formula

G.f.: x*(2 + 3*x - 2*x^2 - x^3 + 4*x^4 + 10*x^5 - 14*x^6 - 32*x^7 - 29*x^8 - 2*x^9 - 21*x^10 - 140*x^11 - 140*x^12 + 126*x^13 + 80*x^14 + 127*x^15 + 143*x^16 + 695*x^17 + 401*x^18 + 462*x^19 + 582*x^20 - 8*x^21 - 490*x^22 - 660*x^23 - 721*x^24 - 960*x^25 - 714*x^26 - 925*x^27 + 25*x^28 + 206*x^29 + 255*x^30 + 494*x^31 + 155*x^32 + 443*x^33 - 118*x^34 + 80*x^35 - 71*x^36 - 172*x^37 + 78*x^38 - 105*x^39 + 79*x^40 + 7*x^41 - 28*x^42 + 33*x^43 - 7*x^44 - 4*x^45 + 3*x^46 - x^47) / (1 - 2*x - 2*x^2 - 4*x^3 + 8*x^4 - 2*x^5 - 2*x^6 - 23*x^7 + 14*x^8 + 31*x^9 + 31*x^10 - 45*x^11 + 50*x^12 + 83*x^13 + 122*x^14 - 141*x^15 - 54*x^16 - 105*x^17 + 36*x^18 - 85*x^19 - 275*x^20 - 222*x^21 + 63*x^22 + 90*x^23 - 140*x^24 + 253*x^25 + 399*x^26 + 234*x^27 + 190*x^28 - 87*x^29 + 59*x^30 - 219*x^31 - 222*x^32 - 189*x^33 - 270*x^34 + 152*x^35 + 56*x^36 + 123*x^37 + 158*x^38 - 41*x^39 + 75*x^40 - 62*x^41 - 12*x^42 + 21*x^43 - 30*x^44 + 7*x^45 + 4*x^46 - 3*x^47 + x^48) (conjectured). - Colin Barker, Aug 02 2017

a(n) = Sum_{k=1..48} c(k)*a(n-k), where c = (2, 2, 4, -8, 2, 2, 23, -14, -31, -31, 45, -50, -83, -122, 141, 54, 105, -36, 85, 275, 222, -63, -90, 140, -253, -399, -234, -190, 87, -59, 219, 222, 189, 270, -152, -56, -123, -158, 41, -75, 62, 12, -21, 30, -7, -4, 3, -1) (conjectured). - Eric W. Weisstein, Aug 02 2017