A287474 -id:A287474 - cp's OEIS frontend

A290381 Number of minimal dominating sets in the n-web graph.

22, 53, 146, 338, 995, 2661, 6961, 18770, 50161, 134426, 359126, 960419, 2570837, 6875493, 18392182, 49200125, 131613970, 352077098, 941809667, 2519398997, 6739522745, 18028532346, 48227208121, 129010104410, 345108392014, 923181669827, 2469555755813

Offset: 3

Eric W. Weisstein, Jul 28 2017

nonn

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, Web Graph

Cf. A287474, A290336.

Empirical: a(n) = a(n-1)+2*a(n-2)+5*a(n-3) +4*a(n-4)+4*a(n-5)-8*a(n-6) for n>8. - Andrew Howroyd, Aug 01 2017

Empirical g.f.: x^3*(22 + 31*x + 49*x^2 - 24*x^3 + 12*x^4 - 40*x^5) / (1 - x - 2*x^2 - 5*x^3 - 4*x^4 - 4*x^5 + 8*x^6). - Colin Barker, Aug 01 2017

Terms a(7) and beyond from Andrew Howroyd, Aug 01 2017

A290591 Number of irredundant sets in the n-web graph.

Original entry on oeis.org

4, 22, 112, 618, 3044, 14026, 70340, 347074, 1713820, 8430362, 41516292, 204628626, 1008216460, 4967464650, 24473678612, 120581823170, 594106884060, 2927147525626, 14421969381220, 71056635221618, 350094259434668, 1724905262555178, 8498562511858612

Offset: 1

Eric W. Weisstein, Aug 07 2017

nonn

The n-web graph is well defined for n >= 3. Sequence extended to n=1 via the number of period n periodic solutions on a larger graph. - Andrew Howroyd, Aug 07 2017

Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Irredundant Set
Eric Weisstein's World of Mathematics, Web Graph

Cf. A287474, A290381.

From Andrew Howroyd, Aug 07 2017: (Start)
Empirical: a(n) = 4*a(n-1) + 3*a(n-2) + 4*a(n-3) + 22*a(n-4) + 12*a(n-5) - 164*a(n-6) + 80*a(n-7) - 24*a(n-8) + 80*a(n-9) for n > 9.
Empirical g.f.: 2*x*(2 + 3*x + 6*x^2 + 44*x^3 + 30*x^4 - 492*x^5 + 280*x^6 - 96*x^7 + 360*x^8)/(1 - 4*x - 3*x^2 - 4*x^3 - 22*x^4 - 12*x^5 + 164*x^6 - 80*x^7 + 24*x^8 - 80*x^9).
(End)

a(1)-a(2) and terms a(8) and beyond from Andrew Howroyd, Aug 07 2017

cp's OEIS Frontend

A290381 Number of minimal dominating sets in the n-web graph.

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