A389184 - OEIS

%I #24 Mar 02 2026 16:16:46

%S 54,181,311,892,1247,3153,3814,8806,9648,20749,21425,43450,43221,

%T 83329,80938,149278,142786,253221,239821,410730,386539,641697,601526,

%U 971062,908164,1429597,1335393,2054746,1918529,2891521,2700138,3993454,3730966,5423605,5070925,7255626,6790135,9574881

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

%C Mutual-visibility sets in the n-prism graph have at most 6 vertices. - _Andrew Howroyd_, Jan 11 2026

%H Andrew Howroyd, <a href="/A389184/b389184.txt">Table of n, a(n) for n = 3..1000</a>

%H Andrew Howroyd, <a href="/A389184/a389184.txt">Visibility polynomial is the n-prism graph</a>, Feb 2026.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VisibilityPolynomial.html">Visibility Polynomial</a>.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

%F From _Andrew Howroyd_, Jan 11 2026: (Start)

%F 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.

%F 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.

%F 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)

%o (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

%Y Cf. A389177.

%K nonn,easy

%O 3,1

%A _Eric W. Weisstein_, Sep 25 2025

%E a(27) onward from _Andrew Howroyd_, Jan 11 2026