A389180 Number of mutual-visibility sets in the n-helm graph.

57, 159, 380, 836, 2293, 6682, 19819, 59200, 177313, 531622, 1594519, 4783180, 14349133, 43046962, 129140419, 387420760, 1162261753, 3486784702, 10460353519, 31381059940, 94143179173, 282429536842, 847288609819, 2541865828720, 7625597485393, 22876792455382

Offset

3,1

Comments

For n >= 7, the visibility polynomial is (1 + 2*x)^n + x + n*x^2*(1 + 2*x)*(3 + 2*x). - Andrew Howroyd, Dec 27 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 3..1000

Andrew Howroyd, Visibility polynomial of n-helm graph, Jan 2026.

Eric Weisstein's World of Mathematics, Helm Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Formula

From Andrew Howroyd, Dec 27 2025: (Start)

a(n) = 3^n + 15*n + 1 for n >= 7.

G.f.: x^3*(57 - 126*x - 16*x^2 - 122*x^3 + 296*x^4 - 71*x^5 - 48*x^6)/((1 - x)^2*(1 - 3*x)). (End)

Prog

(PARI) a(n) = if(n < 7, [57, 159, 380, 836][n-2], 3^n + 15*n + 1) \\ Andrew Howroyd, Dec 27 2025

Crossrefs

Sequence in context: A356423 A044389 A044770 * A008877 A381766 A338078

Adjacent sequences: A389177 A389178 A389179 * A389181 A389182 A389183

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 25 2025

Extensions

a(13)-a(14) from Eric W. Weisstein, Oct 20 2025

a(15) onward from Andrew Howroyd, Dec 27 2025

Status

approved