A290510 Number of irredundant sets in the n-antiprism graph.

1, 5, 22, 37, 76, 194, 491, 1125, 2731, 6640, 15962, 38386, 92639, 223403, 538102, 1297061, 3126726, 7535759, 18162481, 43777272, 105514634, 254314406, 612962766, 1477397778, 3560896401, 8582652759, 20686361179, 49859334611, 120173522734, 289648431514

Offset: 1

Author

Eric W. Weisstein, Aug 04 2017

Keywords

• nonn

Comments

The n-antiprism graphs are well defined for n>=3. Sequence extendend to n=1 using recurrence. - Andrew Howroyd, Aug 05 2017

Links

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

Crossrefs

Cf. A284699, A290377.

Formula

Empirical: a(n) = a(n-1)+2*a(n-2)+5*a(n-3) -6*a(n-5)-10*a(n-6) +6*a(n-8)+10*a(n-9)-a(n-10) -2*a(n-11)-5*a(n-12)+a(n-15) for n>15. - Andrew Howroyd, Aug 05 2017

Empirical g.f.: x*(1 + 4*x + 15*x^2 - 30*x^4 - 60*x^5 + 48*x^7 + 90*x^8 - 10*x^9 - 22*x^10 - 60*x^11 + 15*x^14) / ((1 - x)*(1 + x + x^2)*(1 - x - 2*x^2 - 4*x^3 - x^4 + 4*x^5 + 6*x^6 - x^7 - 2*x^8 - 4*x^9 + x^12)). - Colin Barker, Aug 05 2017

Extensions

a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Aug 05 2017