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

3,1

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

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

Crossrefs

Cf. A284702, A290337, A290379.

Sequence in context: A041252 A041250 A225299 * A300405 A248323 A291059

Adjacent sequences: A290333 A290334 A290335 * A290337 A290338 A290339

Keyword

nonn

Author

Eric W. Weisstein, Jul 27 2017

Extensions

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

Status

approved