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

1,2

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

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

Crossrefs

Cf. A284699, A290377.

Sequence in context: A288676 A085101 A350120 * A184724 A082005 A273024

Adjacent sequences: A290507 A290508 A290509 * A290511 A290512 A290513

Keyword

nonn

Author

Eric W. Weisstein, Aug 04 2017

Extensions

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

Status

approved