A290336 Number of minimal dominating sets in the n-prism graph.

11, 12, 37, 55, 149, 316, 596, 1219, 2444, 4971, 10103, 20465, 41746, 84924, 172501, 350668, 712597, 1448447, 2943959, 5983344, 12162310, 24720787, 50246512, 102129655, 207584129, 421928981, 857596064, 1743117100, 3543000201, 7201373724, 14637255611

Offset: 3

Author

Eric W. Weisstein, Jul 27 2017

Keywords

• nonn

Comments

The prism graphs are defined for n>=3. If the sequence is extended to n=1 using P_n X P_2 then a(1)=2 and a(2)=6 (as A290379). The empirical recurrence is the same as that for the Moebius ladder graph (see A290337). - Andrew Howroyd, Aug 01 2017

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..200
• Eric Weisstein's World of Mathematics, Minimal Dominating Set
• Eric Weisstein's World of Mathematics, Prism Graph

Crossrefs

Cf. A284702, A290337, A290379.

Formula

Empirical: a(n) = a(n-1)+a(n-2)+2*a(n-3) -a(n-4)+2*a(n-5)-2*a(n-6) +6*a(n-7)+4*a(n-8)+4*a(n-9) -6*a(n-10)-3*a(n-12) +5*a(n-13)-a(n-14)-2*a(n-15) -5*a(n-16)-2*a(n-17)-2*a(n-18) for n > 20. - Andrew Howroyd, Aug 01 2017

Empirical g.f.: x^3*(11 + x + 14*x^2 - 16*x^3 + 44*x^4 + 28*x^5 + 56*x^6 - 52*x^7 - 6*x^8 - 70*x^9 + 52*x^10 - 28*x^11 - 23*x^12 - 97*x^13 - 56*x^14 - 62*x^15 - 12*x^16 - 8*x^17) / ((1 - x)*(1 + 2*x^4 + x^6)*(1 - x^2 - 3*x^3 - 4*x^4 - 4*x^5 - x^6 - 2*x^7 - 3*x^8 - 5*x^9 - 4*x^10 - 2*x^11)). - Colin Barker, Aug 02 2017

Extensions

Terms a(9) and beyond from Andrew Howroyd, Aug 01 2017