A389184 Number of mutual-visibility sets in the n-prism graph.

54, 181, 311, 892, 1247, 3153, 3814, 8806, 9648, 20749, 21425, 43450, 43221, 83329, 80938, 149278, 142786, 253221, 239821, 410730, 386539, 641697, 601526, 971062, 908164, 1429597, 1335393, 2054746, 1918529, 2891521, 2700138, 3993454, 3730966, 5423605, 5070925, 7255626, 6790135, 9574881

Offset

3,1

Comments

Mutual-visibility sets in the n-prism graph have at most 6 vertices. - Andrew Howroyd, Jan 11 2026

Links

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

Andrew Howroyd, Visibility polynomial is the n-prism graph, Feb 2026.

Eric Weisstein's World of Mathematics, Prism Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

Formula

From Andrew Howroyd, Jan 11 2026: (Start)

a(n) = (7*n^6 + 135*n^5 + 730*n^4 + 11370*n^3 - 43937*n^2 + 83535*n + 5760)/5760 for odd n >= 7.

a(n) = (7*n^6 + 210*n^5 + 1660*n^4 + 14040*n^3 - 117632*n^2 + 384000*n + 5760)/5760 for even n >= 10.

G.f.: x^3*(54 + 127*x - 194*x^2 - 181*x^3 + 385*x^4 + 325*x^5 - 599*x^6 - 269*x^7 + 411*x^8 + 24*x^9 + 65*x^10 + 132*x^11 - 276*x^12 - 136*x^13 + 198*x^14 + 72*x^15 - 82*x^16 - 16*x^17 + 16*x^18)/((1 - x)^7*(1 + x)^6). (End)

Prog

(PARI) a(n) = if(n<9, [8, -32, 10, -14, 0, -16][n-2]) + if(n%2, 7*n^6 + 135*n^5 + 730*n^4 + 11370*n^3 - 43937*n^2 + 83535*n + 5760, 7*n^6 + 210*n^5 + 1660*n^4 + 14040*n^3 - 117632*n^2 + 384000*n + 5760)/(5760) \\ Andrew Howroyd, Jan 11 2026

Crossrefs

Cf. A389177.

Sequence in context: A044980 A248598 A157428 * A187299 A288626 A124007

Adjacent sequences: A389181 A389182 A389183 * A389185 A389186 A389187

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 25 2025

Extensions

a(27) onward from Andrew Howroyd, Jan 11 2026

Status

approved