A392237 Number of maximal irredundant sets in the n-double cone graph.

1, 5, 10, 37, 101, 122, 197, 197, 901, 3845, 4357, 9802, 20450, 44945, 117650, 228485, 485810, 984065, 2253002, 5044517, 10569002, 22810177, 48566962, 105740090, 231344101, 497156210, 1071056530, 2302464257, 4990574737, 10807889522, 23319122437, 50347281925

Offset

1,2

Comments

Sequence extended to a(1) using the formula. - Eric W. Weisstein, Jan 13 2026

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Double Cone Graph.

Eric Weisstein's World of Mathematics, Maximal Irredundant Set.

Formula

a(n) = A286954(n)^2 + 1. - Christian Sievers, Jan 07 2026

Mathematica

Table[RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, #^n &]^2 + 1, {n, 20}] (* Eric W. Weisstein, Jan 13 2026 *)
RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, #^Range[20] &]^2 + 1 (* Eric W. Weisstein, Jan 13 2026 *)

Prog

(PARI) a(n)=polsym(1-x^3-2*x^4+x^5+2*x^6+x^7-x^9-x^10-x^11-x^12+x^14, n)[n+1]^2+1 \\ Christian Sievers, Jan 07 2026

Crossrefs

Cf. A286954, A291063, A391917.

Sequence in context: A189732 A307607 A174933 * A270219 A270276 A271604

Adjacent sequences: A392234 A392235 A392236 * A392238 A392239 A392240

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 04 2026

Extensions

a(15) onward from Christian Sievers, Jan 07 2026

a(1)-a(2) prepended by Eric W. Weisstein, Jan 13 2026

Status

approved