A288030 Number of minimal edge covers in the grid graph P_3 X P_n.

1, 6, 38, 190, 1021, 5494, 29042, 154772, 824695, 4386942, 23356322, 124344111, 661873859, 3523418150, 18756407661, 99845472493, 531509598443, 2829393615575, 15061734439895, 80178331797652, 426814323111204, 2272065745374039, 12094915689644237

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Edge Cover

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Formula

Empirical: a(n) = 3*a(n-1)+6*a(n-2)+35*a(n-3) -7*a(n-4)+15*a(n-5)-55*a(n-6) +31*a(n-7)+36*a(n-8)+36*a(n-9) -124*a(n-10)-8*a(n-12)+32*a(n-13) +a(n-14)+9*a(n-15)-2*a(n-16) -2*a(n-17)-a(n-18) for n>18.

Empirical g.f.: x*(1 + 3*x + 14*x^2 + 5*x^3 + 20*x^4 - 12*x^5 + 15*x^6 + 6*x^7 + 2*x^8 - 82*x^9 - 5*x^10 - 3*x^11 + 29*x^12 + 8*x^14 - 2*x^15 - 2*x^16 - x^17) / (1 - 3*x - 6*x^2 - 35*x^3 + 7*x^4 - 15*x^5 + 55*x^6 - 31*x^7 - 36*x^8 - 36*x^9 + 124*x^10 + 8*x^12 - 32*x^13 - x^14 - 9*x^15 + 2*x^16 + 2*x^17 + x^18). - Colin Barker, Jun 16 2017

Crossrefs

Row 3 of A288025.

Cf. A288029, A288027.

Sequence in context: A045949 A189492 A281803 * A264502 A263331 A026296

Adjacent sequences: A288027 A288028 A288029 * A288031 A288032 A288033

Keyword

nonn

Author

Andrew Howroyd, Jun 04 2017

Status

approved